| Type: | Package |
| Title: | Periodically Correlated and Periodically Integrated Time Series |
| Description: | Classes and methods for modelling and simulation of periodically correlated (PC) and periodically integrated time series. Compute theoretical periodic autocovariances and related properties of PC autoregressive moving average models. Some original methods including Boshnakov & Iqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>, Boshnakov (1996) <doi:10.1111/j.1467-9892.1996.tb00281.x>. |
| Version: | 0.15.8 |
| Depends: | R (≥ 3.5.0), methods |
| Imports: | sarima, Matrix (≥ 1.5-0), BB, PolynomF (≥ 2.0-2), gbutils,zoo, xts, stats4, lagged (≥ 0.2.2), mcompanion (≥ 0.5.8),Rdpack (≥ 0.9), lubridate |
| Suggests: | testthat, fUnitRoots, knitr, rmarkdown |
| RdMacros: | Rdpack |
| LazyData: | yes |
| URL: | https://geobosh.github.io/pcts/ (doc)https://github.com/GeoBosh/pcts/ (devel) |
| BugReports: | https://github.com/GeoBosh/pcts/issues |
| License: | GPL-2 |GPL-3 [expanded from: GPL (≥ 2)] |
| Collate: | utils.R test1.r PeriodicCalc.R pcstat.R pc00smallutil.rpc02filters.r pc03simu.r acfsums.R pcls.R pcarma_model.Rpcarma_acf.R generics.R autocovariances.R classCycle.RpcFilterClasses.R PeriodicClasses.R cyclic.RFittedPeriodicModels.R fitPM.R pcTest.R PeriodicVector.R sim.Roptimcore.R trig.R |
| RoxygenNote: | 7.1.1 |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-03-17 09:33:01 UTC; georgi |
| Author: | Georgi N. Boshnakov [aut, cre] |
| Maintainer: | Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk> |
| Repository: | CRAN |
| Date/Publication: | 2025-03-17 11:00:02 UTC |
Periodically Correlated and Periodically Integrated Time Series
Description
Classes and methods for modelling and simulation of periodically correlated (PC) and periodically integrated time series. Compute theoretical periodic autocovariances and related properties of PC autoregressive moving average models. Some original methods including Boshnakov & Iqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>, Boshnakov (1996) <doi:10.1111/j.1467-9892.1996.tb00281.x>.
Details
The underlying assumption is that the observations are made at regularintervals, such as quarter, month, week, day — or represent data forsuch intervals — and these intervals are nested into larger periods.In pcts we call the larger period a cycle and its parts seasons. Typicalexamples of season-cycle timing are months in a year, quarters in ayear, days in a week (or business week). The number of seasons in acycle is called frequency in class"ts" in baseR.
Cycles in pcts keep not only the number of seasons (frequency) but otherinformation, such as the names of the seasons and units of seasons. Inpcts there are a number of builtin cycle classes for typical cases, aswell as provision for creation of custom cycles on the fly. SeepcCycle andBuiltinCycle for ways to createcycle objects, andallSeasons for further examples.
Periodic time series can be created withpcts, whichaccepts as input vectors, matrices and time series objects from base Rand some other packages, including zoo and xts. When importing data,the time information is taken from the data and an attempt is made toguess the periodicity from the frequency (for time series objects thathave it set) and an analysis of the datetime stamps, if present.pcts also has arguments for specifying the number of seasons orthe cycle, as well as the start datetime.
The main periodic time series classes inpcts arePeriodicTS andPeriodicMTS,for univariate and multivariate time series, respectively. Standardbase-R time series functions can be used with them directly, see forexamplewindow,frequency,cycle,time,deltat,start,end,boxplot,monthplot,na.trim (na.trim is from packagezoo).
Methods forplot,summary,print,show,head,tail,and other base-R functions are defined where suitable. Examples can befound in section Examples and in help pages for the correspondingfunctions, classes and methods.
The naming conventions are as follows. Names of classes generallyconsists of one or more words. The first letter of each word, iscapitalised. Only the first letter of abbreviations for models, such asARMA, is capitalised. Similarly for generic functions but for them thefirst word is not capitalised. In a few names PM stands for 'periodicmodel' and TS for 'time series'.
Significant portion of the code was written in 2005–2007. Many of thefunctions and classes have been renamed under the aboveconventions and most of those that are not are not exported but a fewstill are and they should be considered subject to change.
autocovariances,autocorrelations,partialAutocorrelationsand others are one-stop generic functions for computation of propertiesof time series and models. What to compute is deduced from the type ofthe object. For models they compute theoretical quantities — periodicor non-periodic, scalar or multivariate. For time series they computethe corresponding sample counterparts.
Author(s)
Georgi N. Boshnakov [aut, cre] (<https://orcid.org/0000-0003-2839-346X>)
Maintainer: Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>
References
Boshnakov GN (1994).“Periodically Correlated Sequences: Some Properties and Recursions.”Research Report 1, Division of Quality Technology and Statistics, Luleo University, Sweden.
Boshnakov GN (1996).“The asymptotic covariance matrix of the multivariate serial correlations.”Stochastic Process. Appl.,65(2), 251–258.ISSN 0304-4149,doi:10.1016/S0304-4149(96)00104-4.
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
Boshnakov GN (1997).“Periodically correlated solutions to a class of stochastic difference equations.”In Csiszar I, Michaletzky G (eds.),Stochastic differential and difference equations (Gyor, 1996), volume 23 ofProgr. Systems Control Theory, 1–9.Birkhauser Boston, Boston, MA.
Boshnakov GN (2002).“Multi-companion matrices.”Linear Algebra Appl.,354, 53–83.ISSN 0024-3795,doi:10.1016/S0024-3795(01)00475-X.
Boshnakov GN, Boteva A (1992).“An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.”Varna.
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
Boshnakov GN, Iqelan BM (2012).“Maximum entropy models for general lag patterns.”Journal of Time Series Analysis,33(1), 112–120.ISSN 1467-9892,doi:10.1111/j.1467-9892.2011.00744.x.
Boshnakov GN, Lambert-Lacroix S (2009).“Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients.”J. Time Series Anal.,30(5), 467–486.doi:10.1111/j.1467-9892.2009.00619.x.
Boshnakov GN, Lambert-Lacroix S (2011).pcme: Maximum entropy estimation of periodically correlated time series.R package version 0.55,https://personalpages.manchester.ac.uk/staff/georgi.boshnakov/Rpackages/.
Boshnakov GN, Lambert-Lacroix S (2012).“A periodic Levinson-Durbin algorithm for entropy maximization.”Computational Statistics & Data Analysis,56, 15–24.ISSN 0167-9473,doi:10.1016/j.csda.2011.07.001.
Boswijk HP, Franses PH (1996).“Unit roots in periodic autoregressions.”Journal of Time Series Analysis,17(3), 221–245.
Francq C, Roy R, Saidi A (2011).“Asymptotic properties of weighted least squares estimation in weak parma models.”Journal of Time Series Analysis,32(6), 699–723.
Franses PH (1996).Periodicity and Stochastic Trends In Economic Time Series.Oxford University Press Inc., New York.
Franses PH, Paap R (2004).Periodic Time Series Models.Oxford University Press Inc., New York.
Grolemund G, Wickham H (2011).“Dates and Times Made Easy with lubridate.”Journal of Statistical Software,40(3), 1–25.doi:10.18637/jss.v040.i03.
Hipel KW, McLeod AI (1994).Time series modelling of water resources and environmental systems, Developments in water science; 45.London; Amsterdam: Elsevier.
Lambert-Lacroix S (2000).“On periodic autoregressive process estimation.”IEEE Transactions on Signal Processing,48(6), 1800-1803.
Lambert-Lacroix S (2005).“Extension of autocovariance coefficients sequence for periodically correlated processes.”Journal of Time Series Analysis,26(3), 423-435.
Lancaster P, Tismenetsky M (1985).The theory of matrices, Second edition.Academic Press, New York.
McLeod AI (1993).“Parsimony, model adequacy and periodic correlation in time series forecasting.”Internat. Statist. Rev.,61(3), 387-393.
McLeod AI (1993).“Parsimony, model adequacy and periodic correlation in time series forecasting.”Internat. Statist. Rev.,61(3), 387-393.
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
McLeod AI (1995).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,16(6), 647-648.doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
Pagano M (1978).“On periodic and multiple autoregression.”Ann. Statist.,6, 1310-1317.
See Also
pcts,
dataFranses1996,Fraser2017,four_stocks_since2016_01_01,
Examples
data(dataFranses1996) class(dataFranses1996) # [1] "mts" "ts" "matrix"pcfr <- pcts(dataFranses1996)class(pcfr) # "PeriodicMTS"nSeasons(pcfr) # 4allSeasons(pcfr)allSeasons(pcfr, abb = TRUE)## subsetting## one index, x[i], is analogous to listspcfr2to4 <- pcfr[2:4]; class(pcfr2to4) # "PeriodicMTS"pcfr2to2 <- pcfr[2]; class(pcfr2to2) # "PeriodicMTS"pcfr2 <- pcfr[[2]]; class(pcfr2) # note '[[', "PeriodicTS"## data for 1990 quarter 3pcfr2to4[as_date("1990-07-01")] # note: not "1990-03-01"!pct1990_Q3 <- Pctime(c(1990, 3), pcCycle(pcfr2to4))pcfr2to4[pct1990_Q3]## with empty index, returns the underlying datadim(pcfr[]) # [1] 148 19dim(pcfr2to2[]) # 148 1length(pcfr2[]) # 148 (this is numeric)summary(pcfr2)summary(pcfr2to4)## make the output width shortersummary(pcfr2to4, row.names = FALSE)summary(pcfr2to4, row.names = 5) # trim row names to 5 charactershead(pcfr2to4) # starts with NA'stail(pcfr2to4) # some NA's at the end too## time of first and last data, may be NA'sstart(pcfr2to4) # 1955 Q1end(pcfr2to4) # 1991 Q4## time of first nonNA:availStart(pcfr2) # 1955 Q1availStart(pcfr2to4) # 1955 Q1## time of last nonNA:availEnd(pcfr[[2]]) # 1991 Q4availEnd(pcfr[[3]]) # 1987 Q4availEnd(pcfr[[4]]) # 1990 Q4## but at least one of them is available for 1991 Q4, so:availEnd(pcfr2to4) # 1991 Q4## use window() to pick part of the ts by time:window(pcfr2to4, start = c(1990, 1), end = c(1991, 4))## drop NA's at the start and end:window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4))plot(pcfr2) # the points mark the first season in each cycleboxplot(pcfr2)monthplot(pcfr2)Methods for function$ in package 'pcts'
Description
Methods for function$ in package 'pcts'.
Methods
signature(x = "PeriodicMTS")
Class BareCycle
Description
Class BareCycle.
Objects from the Class
Objects can be created by calls of the formpcCycle(nseasons)ornew("BareCycle", nseasons).
Class"BareCycle" represents the number of seasons and issufficient for many computations.
Slots
nseasons:Object of class
"integer", the numberof seasons.
Extends
Class"BasicCycle", directly.
Methods
- initialize
signature(.Object = "BareCycle"): ...- coerce
signature(from = "BareCycle", to = "SimpleCycle"): ...- coerce
signature(from = "BuiltinCycle", to = "BareCycle"): ...- nSeasons
signature(object = "BareCycle"): ...- show
signature(object = "BareCycle"): ...
Author(s)
Georgi N. Boshnakov
See Also
pcCycle for creation of cycle objects and extraction ofcycle part of time series,
BuiltinCycle-class,SimpleCycle-class,
DayWeekCycle-class,MonthYearCycle-class,OpenCloseCycle-class,QuarterYearCycle-classPartialCycle-class,
BasicCycle-class (virtual, for use in signatures)
Examples
pcCycle(5)cycle <- new("BareCycle", 5)identical(new("BareCycle", 5), pcCycle(5)) # TRUEunitSeason(cycle)unitCycle(cycle)allSeasons(cycle)seqSeasons(cycle)cycle[]cycle[3]## if cycle represents 5-days week one may prefer:BuiltinCycle(5)Class BasicCycle
Description
Virtual class"BasicCycle" is a class union that can be used insignatures of methods and classes when any of the cycle classes isadmissible as argument or slot.
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
- [
signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")- [
signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")- [<-
signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")- [<-
signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")- date<-
signature(x = "BasicCycle"): ...- allSeasons
signature(x = "BasicCycle", abb = "ANY")- seqSeasons
signature(x = "BasicCycle")- pcCycle
signature(x = "BasicCycle", type = "character"): ...- pcCycle
signature(x = "BasicCycle", type = "missing"): ...- pcts
signature(x = "matrix", nseasons = "BasicCycle"): ...- pcts
signature(x = "numeric", nseasons = "BasicCycle"): ...
Author(s)
Georgi N. Boshnakov
See Also
BareCycle-class (just number of seasons),
SimpleCycle-class (named seasons),
BuiltinCycle-class (common cycles, e.g.,DayWeekCycle-class,MonthYearCycle-class,OpenCloseCycle-class,QuarterYearCycle-class),
PartialCycle-class (cycles obtained from others bysubsetting or otherwise)
Examples
showClass("BasicCycle")Class"BuiltinCycle" and its subclasses in package 'pcts'
Description
Class"BuiltinCycle" and its subclasses in package 'pcts'.
Objects from the Class
Class"BuiltinCycle" is a virtual Class: no objects may becreated from it. Class"BuiltinCycle" has several built-incycle subclasses. Objects from the subclasses can be created by callsof the formnew("className", first, ...), where"className" is the name of the subclass. The optional argumentfirst can be used to designate a season to be considered firstin the cycle, by default the first.
The functionBuiltinCycle provides a more convenient wayto generate objects from subclasses of class"BuiltinCycle". Its argument is the number of seasons.
These classes are effectively unmodifiable, but the user can convertthem to other cycle classes, e.g. class "SimpleCycle", and adapt asneeded.
The subclasses of"BuiltinCycle" have definitions for allmethods promised by its superclass"BasicCycle".
Currently, the following builtin classes are defined:
| Name | Description | nSeasons |
"DayWeekCycle" | weekdays | 7 |
"QuarterYearCycle" | quarters in a year | 4 |
"MonthYearCycle" | months in a year | 12 |
"Every30MinutesCycle" | half-hour intervals in a day | 48 |
"OpenCloseCycle" | start/end of a working day | 2 |
There is also a class"FiveDayWeekCycle" but it is deprecatedand will be removed in the near future. UseBuiltinCycle(5)to create objects with equivalent functionality.
Slots
The class"BuiltinCycle" and its subclasses have a singlecommon slot:
first:Object of class
"integer",the index of the season to be treated as the first in a cycle.
Extends
Class"BuiltinCycle" extends class"BasicCycle", directly.
Classes"DayWeekCycle","Every30MinutesCycle","FiveDayWeekCycle","OpenCloseCycle" and"QuarterYearCycle" extend:
Class"BuiltinCycle", directly.Class"BasicCycle", by class "BuiltinCycle", distance 2.
Methods
Functions with methods for this class:
- coerce
signature(from = "BuiltinCycle", to = "BareCycle"): ...- coerce
signature(from = "BuiltinCycle", to = "SimpleCycle"): ...- initialize
signature(.Object = "BuiltinCycle"): ...- show
signature(object = "BuiltinCycle"): ...
The functions to extract properties from objects from the builtincycle classes have identical signatures (except for the name of theclass). For example, for"QuarterYearCycle" the methods are asfollows:
- allSeasons
signature(x = "QuarterYearCycle", abb = "logical"): ...- allSeasons
signature(x = "QuarterYearCycle", abb = "missing"): ...- nSeasons
signature(object = "QuarterYearCycle"): ...- unitCycle
signature(x = "QuarterYearCycle"): ...- unitSeason
signature(x = "QuarterYearCycle"): ...
The methods for the remaining builtin classes are the same with"QuarterYearCycle" replaced suitably.
Author(s)
Georgi N. Boshnakov
See Also
BuiltinCycle,pcCycle for creation of cycle objects and extraction ofcycle part of time series,
classPartialCycle for creating variants of thebuiltin classes, e.g., 5-day weeks.
BareCycle-class,SimpleCycle-class,
Examples
## class "DayWeekCycle"dwcycle <- BuiltinCycle(7) # new("DayWeekCycle")unitSeason(dwcycle)unitCycle(dwcycle)allSeasons(dwcycle)dwcycle[] # sameallSeasons(dwcycle, abb = TRUE)dwcycle[ , abb = TRUE] # samedwcycle[2]dwcycle[2, abb = TRUE]seqSeasons(dwcycle)## start the week on Sundaydws <- BuiltinCycle(7, first = 7) # new("DayWeekCycle", first = 7)dws[1] # "Sunday"allSeasons(dws)## class "Every30MinutesCycle"cyc48 <- BuiltinCycle(48) # new("Every30MinutesCycle")nSeasons(cyc48)allSeasons(cyc48)## class "FiveDayWeekCycle" is deprecated, use the equivalent:fdcycle <- BuiltinCycle(5)unitSeason(fdcycle)unitCycle(fdcycle)allSeasons(fdcycle)fdcycle[] # sameallSeasons(fdcycle, abb = TRUE)fdcycle[ , abb = TRUE] # samefdcycle[2]fdcycle[2, abb = TRUE]seqSeasons(fdcycle)## class "MonthYearCycle"mycycle <- BuiltinCycle(12) # new("MonthYearCycle")unitSeason(mycycle)unitCycle(mycycle)allSeasons(mycycle)mycycle[ ] # sameallSeasons(mycycle, , abb = TRUE)mycycle[ , abb = TRUE] # samemycycle[2]mycycle[2, abb = TRUE]seqSeasons(mycycle)## class "OpenCloseCycle"opcycle <- new("OpenCloseCycle")unitSeason(opcycle)unitCycle(opcycle)allSeasons(opcycle)opcycle[ , abb = FALSE] # sameallSeasons(opcycle, abb = FALSE)opcycle[] # sameopcycle[2]opcycle[2, abb = TRUE]seqSeasons(opcycle)## class "QuarterYearCycle"qycycle <- new("QuarterYearCycle")unitSeason(qycycle)unitCycle(qycycle)allSeasons(qycycle)qycycle[] # sameallSeasons(qycycle, abb = TRUE)qycycle[ , abb = TRUE] # sameqycycle[2]qycycle[2, abb = TRUE]seqSeasons(qycycle)Create objects from class Cyclic
Description
Create objects from class Cyclic.
Usage
Cyclic(cycle, start = NULL, ...)## S3 method for class 'Cyclic'as.Date(x, ...)## S3 method for class 'Cyclic'date(x)## S3 method for class 'PeriodicTimeSeries'as.Date(x, ...)Arguments
cycle | a cycle object, a positive integer giving the number of seasons, orany other object that can be used to create a cycle with |
start | a cycle-season pair, a datetime object, a Date object or any objectthat can be converted to datetime with |
... | for |
x | a Cyclic object |
Value
forCyclic, an object from class"Cyclic"
See Also
BuiltinCycle,pcCycle for creation of cycle objects,
pcts importing and creating periodic time series
Examples
## bare bone Cyclic starting at Cycle 1, season 1Cyclic(4) Cyclic(4, c(1,1)) # same## with quarter/year cyclequ <- Cyclic(BuiltinCycle(4), start = c(2020, 1))start(qu)as_datetime(qu)date(qu) <- c(2009, 2)quap <- pcts(AirPassengers)as.Date(ap)Class"Cyclic"
Description
Class"Cyclic"
Objects from the Class
Objects can be created by calls of the formnew("Cyclic", ...).
Slots
cycle:Object of class
"BasicCycle"~~pcstart:Object of class
"ANY"~~
Methods
- allSeasons
signature(x = "Cyclic", abb = "ANY"): ...- allSeasons<-
signature(x = "Cyclic"): ...- as_date
signature(x = "Cyclic"): ...- coerce
signature(from = "PeriodicMTS", to = "Cyclic"): ...- coerce
signature(from = "PeriodicTS", to = "Cyclic"): ...- coerce<-
signature(from = "PeriodicMTS", to = "Cyclic"): ...- coerce<-
signature(from = "PeriodicTS", to = "Cyclic"): ...- date<-
signature(x = "Cyclic"): ...- nSeasons
signature(object = "Cyclic"): ...- nTicks
signature(x = "Cyclic"): ...- pcCycle
signature(x = "Cyclic", type = "ANY"): ...- seqSeasons
signature(x = "Cyclic"): ...- show
signature(object = "Cyclic"): ...- unitCycle
signature(x = "Cyclic"): ...- unitCycle<-
signature(x = "Cyclic"): ...- unitSeason
signature(x = "Cyclic"): ...- unitSeason<-
signature(x = "Cyclic"): ...
See Also
Pctime for conversion from/to dates and datetimes.
Examples
showClass("Cyclic")Class FittedPeriodicArModel
Description
Class FittedPeriodicArModel.
Objects from the Class
Objects can be created by calls of the formnew("FittedPeriodicArModel", ar, ma, sigma2, ...).
Slots
asyCov:Object of class
"ANY"~~sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~theTS:Object of class
"PeriodicTS"~~ns:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"PeriodicArModel", directly.Class"PeriodicArmaModel", by class "PeriodicArModel", distance 2.Class"VirtualPeriodicArmaModel", by class "PeriodicArModel", distance 3.Class"PeriodicArmaSpec", by class "PeriodicArModel", distance 3.Class"VirtualPeriodicFilterModel", by class "PeriodicArModel", distance 4.Class"VirtualPeriodicStationaryModel", by class "PeriodicArModel", distance 4.Class"VirtualPeriodicAutocovarianceModel", by class "PeriodicArModel", distance 5.Class"VirtualPeriodicMeanModel", by class "PeriodicArModel", distance 5.
Methods
- show
signature(object = "FittedPeriodicArModel"): ...- summary
signature(object = "FittedPeriodicArModel"): ...- as_pcarma_list
signature(object = "FittedPeriodicArModel"): ...
Class FittedPeriodicArmaModel
Description
Class FittedPeriodicArmaModel in package pcts
Objects from the Class
Objects can be created by calls of the formnew("FittedPeriodicArmaModel", ..., mean).
Slots
ar:Object of class
"PeriodicBJFilter"~~ma:Object of class
"PeriodicSPFilter"~~modelCycle:Object of class
"BasicCycle"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~sigma2:Object of class
"numeric"~~theTS:Object of class
"PeriodicTS"~~asyCov:Object of class
"ANY"~~ns:Object of class
"numeric"~~
Extends
Class"PeriodicArmaModel", directly.Class"FittedPM", directly.Class"VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.Class"PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.Class"VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.Class"PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.Class"PeriodicInterceptSpec", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.Class"VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.Class"VirtualArmaFilter", by class "PeriodicArmaModel", distance 4.Class"ModelCycleSpec", by class "PeriodicArmaModel", distance 4.Class"InterceptSpec", by class "PeriodicArmaModel", distance 4.Class"VirtualPeriodicModel", by class "PeriodicArmaModel", distance 5.Class"VirtualMonicFilter", by class "PeriodicArmaModel", distance 5.
Methods
- as_pcarma_list
signature(object = "FittedPeriodicArmaModel"): ...- show
signature(object = "FittedPeriodicArmaModel"): ...
Fraser River at Hope, mean monthly flow
Description
Mean monthly flow (cms) of Fraser River From March 1912 to December2017, recorded by Fraser River at Hope station.
Usage
data("Fraser2017")Format
A time series (class"ts") with frequency 12, starting fromJanuary 1912 (the first two data values areNA) to December 2017.
Details
DatasetFraser2017 is an extention of dataset"Fraser"in package"pear". The latter runs upto December 1990 (not thedocumented December 1991). At the time of writing this package"pear" is archived on CRAN, which is the main reason to includethe dataset (with the added benefit of almost 30 years of additionaldata).
Source
See Also
dataFranses1996,four_stocks_since2016_01_01
Examples
data(Fraser2017)fr <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12))## all.equal(as.numeric(fr), as.numeric(pear::Fraser)) # TRUE## all.equal(tsp(fr), tsp(pear::Fraser)) # TRUEClass LegacyPeriodicFilterModel
Description
Class LegacyPeriodicFilterModel.
Objects from the Class
Objects can be created by calls of the formnew("LegacyPeriodicFilterModel", ...).
Slots
intercept:Object of class
"numeric"~~arFilter:Object of class
"PeriodicArFilter"~~maFilter:Object of class
"PeriodicMaFilter"~~scalesq:Object of class
"numeric"~~jordan:Object of class
"ANY"~~
Extends
Class"VirtualPeriodicFilterModel", directly.
Methods
No methods defined with class "LegacyPeriodicFilterModel" in the signature.
Class ModelCycleSpec
Description
Class ModelCycleSpec.
Objects from the Class
Objects can be created by calls of the formnew("ModelCycleSpec", ...).
Slots
modelCycle:Object of class
"BasicCycle"~~
Methods
- modelCycle
signature(object = "ModelCycleSpec"): ...- modelCycle<-
signature(object = "ModelCycleSpec"): ...
Class PartialCycle
Description
Class PartialCycle
Objects from the Class
Objects can be created by calls of the formnew("PartialCycle", ...).
Partial cycles are often created implicitly when subsetting time seriesusingwindow() with argumentseasons, see the examples.
Slots
orig:the parent class of the partial cycle, an object inheriting fromclass
"BasicCycle".subindex:an integer vector specifying the seasons to include in the partialcycle.
Extends
Class"BasicCycle", directly.
Methods
- allSeasons
signature(x = "PartialCycle", abb = "logical"): ...- allSeasons
signature(x = "PartialCycle", abb = "missing"): ...- nSeasons
signature(object = "PartialCycle"): ...- unitCycle
signature(x = "PartialCycle"): ...- unitSeason
signature(x = "PartialCycle"): ...- show
signature(object = "PartialCycle"): ...
See Also
Examples
dwc <- new("DayWeekCycle")dwcallSeasons(dwc)## a five day week cycledwc5 <- new("PartialCycle", orig = dwc, subindex = 1:5)dwc5allSeasons(dwc5)weekend <- new("PartialCycle", orig = dwc, subindex = 6:7)weekendallSeasons(weekend)ap <- pcts(AirPassengers)## take data for the summer months (in Northern hemisphere)ap7to9 <- window(ap, seasons = 7:9)## the above implicitly creates a partial cycleap7to9allSeasons(ap7to9)Class PartialPeriodicAutocorrelations
Description
Class PartialPeriodicAutocorrelations.
Objects from the Class
Objects can be created by calls of the formnew("PartialPeriodicAutocorrelations", ..., data).
Slots
modelCycle:Object of class
"BasicCycle"~~data:Object of class
"Lagged"~~
Extends
Class"ModelCycleSpec", directly.Class"FlexibleLagged", directly.Class"VirtualPeriodicAutocorrelations", directly.Class"Lagged", by class "FlexibleLagged", distance 2.Class"VirtualPeriodicModel", by class "VirtualPeriodicAutocorrelations", distance 2.
Methods
- show
signature(object = "PartialPeriodicAutocorrelations"): ...
Convert between Pctime and datetime objects
Description
Class"Pctime" is an S3 class inheriting from the base Rdatetime class"POSIXct". It has methods for conversion betweendatetimes and the pcts cycle-season pairs, as well as conveniencemethods for a few other functions.
Usage
Pctime(x, cycle, ...)as_Pctime(x, ...)## S3 method for class 'Pctime'x[i, j, drop = TRUE]## S3 method for class 'Pctime'x[[..., drop = TRUE]]## S3 method for class 'Cyclic'as_Pctime(x, ...)Arguments
x | for |
cycle | a positive integer, cycle object, or missing. |
i | subscript |
j | noi used |
drop | not used |
... | further argument for methods. |
Details
Pctime represents periodic times with cycle specificationcontained in attribute"cycle". It is basically datetime(inheriting from"POSIXct") with additional attribute(s).
For printing Pctime objects are shown as cycle-season pairs. To printin other formats, just convert them usingas_datetime or othersuitable function. Note though that some cycles in pcts do not havenatural datetime representation. For them, Pctime sets it arbitrarillyas the number of seconds from a origin.
The seasons in cycle-season pairs are numbered from one to the numberof seasons. Names and abbreviations are used when available and this isthe case for all builtin cycles and partial cycles obtained from them.
The cycles in cycle-season pairs are numbered from a starting point.For years, it is what is expected. For cycles representing weeks, week 1is the first ISO week of 1970, soc(1,1) corresponds to1969-12-29. For some other cycle classesc(1,1) also correspondsto the first time in the first ISO week of 1970.
Subsetting with"[" keeps thePctime class, while"[[" returns a datetime object. Other standard functions workwith Pctime objects, as well, includingseq.
A common source of frustration is the accidental use ofas.Dateoras_date, instead ofas.POSIXlt oras_datetime.These four are often equivalent, most notably for monthly, quarterly anddaily observations but, in general, conversion to dates drops thefractional day part of a datetime.
The default time zone is UTC. Other time zones can be used since thecalculations use standard datetime and date functions from base R andpackage lubridate (Grolemund and Wickham 2011), but currently this hasnot been tested.
Value
forPctime, an object from S3 class Pctime
References
Grolemund G, Wickham H (2011).“Dates and Times Made Easy with lubridate.”Journal of Statistical Software,40(3), 1–25.doi:10.18637/jss.v040.i03.
Examples
## a bare bone date for four seasonspct4 <- Pctime(c(2020, 2), pcCycle(4))pct4## quarterly cyclePctime("2020-04-01", BuiltinCycle(4))pctQ <- Pctime(c(2020, 2), BuiltinCycle(4)) # samepctQ## day-in-week cycle## c(1, 1) is the start of the first ISO week of 1970weekW1S1 <- Pctime(c(1, 1), BuiltinCycle(7)) # W1 MonweekW1S1as_datetime(weekW1S1)Pctime("1970-01-01", BuiltinCycle(7)) # W1 ThupctW1Th <- Pctime(c(1, 4), BuiltinCycle(7)) # samepctW1ThPctime("2020-04-01", BuiltinCycle(7))pctW2623Wed <- Pctime(c(2623, 3), BuiltinCycle(7)) # samepctW2623Wedas_datetime(pctW2623Wed)## Monday-Friday week - a partial cycle derived from DayOfWeekCycleBuiltinCycle(5)pctMF <- Pctime("2020-04-03", BuiltinCycle(5)) # Friseq(pctMF, length.out = 10) # note: Sat, Sun are skippedPctime("2020-04-04", BuiltinCycle(5)) # Sat, not in the cycle## monthly cyclePctime("2020-04-01", BuiltinCycle(12))pctY2020Apr <- Pctime(c(50, 4), BuiltinCycle(12)) # samepctY2020Apras_datetime(pctW2623Wed)## Pctime can hold a vector of timesap <- pcts(AirPassengers)aptime <- Pctime(ap) # as_Pctime(ap)aptime[1:12] # keep Pctime classaptime[1]aptime[[1]] # drop Pctime classhead(aptime)tail(aptime)apdates <- as_datetime(ap)head(apdates)tail(apdates)Class PeriodicArModel
Description
Class PeriodicArModel.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicArModel", ar, ma, sigma2, ...).
Slots
sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"PeriodicArmaModel", directly.Class"VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.Class"PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.Class"VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.Class"PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.Class"VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.
Methods
- autocovariances
signature(x = "PeriodicArModel", maxlag = "ANY"): ...- coerce
signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...- fitPM
signature(model = "PeriodicArModel", x = "ANY"): ...- fitPM
signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...- fitPM
signature(model = "PeriodicArModel", x = "PeriodicTS"): ...- partialCoefficients
signature(x = "PeriodicArModel"): ...- show
signature(object = "PeriodicArModel"): ...
Create objects from class PeriodicArModel
Description
Create objects from class PeriodicArModel
Usage
PeriodicArModel(object, ...)Arguments
object | an object, can have one of a number of classes. |
... | further arguments for methods. |
Details
PeriodicArModel creates objects from classPeriodicArModel. This is a generic function with dispatch methods onthe first argument.
Value
an object from class"PeriodicArModel"
Methods
signature(object = "matrix")"object"gives the coefficients, one row per season.signature(object = "numeric")"object"gives the model order. Its length is taken to bethe number of seasons. The coefficients are set to NA.signature(object = "PeriodicMonicFilterSpec")signature(object = "VirtualPeriodicArmaModel")signature(object = "PeriodicMonicFilterSpec")signature(object = "VirtualPeriodicArmaModel")
Class"PeriodicArmaFilter"
Description
Class PeriodicArmaFilter.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicArmaFilter", ..., ar, ma, nseasons).
Slots
ar:Object of class
"PeriodicBJFilter"~~ma:Object of class
"PeriodicSPFilter"~~
Extends
Class"VirtualArmaFilter", directly.Class"VirtualMonicFilter", by class "VirtualArmaFilter", distance 2.
Methods
- coerce
signature(from = "PeriodicArmaFilter", to = "PeriodicArFilter"): ...- coerce
signature(from = "PeriodicArmaFilter", to = "PeriodicMaFilter"): ...- initialize
signature(.Object = "PeriodicArmaFilter"): ...- maxLag
signature(object = "PeriodicArmaFilter"): ...- show
signature(object = "PeriodicArmaFilter"): ...
Class PeriodicArmaModel
Description
Class PeriodicArmaModel.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicArmaModel", ar, ma, sigma2, ...).
Slots
sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"VirtualPeriodicArmaModel", directly.Class"PeriodicArmaSpec", directly.Class"VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2.Class"VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2.Class"PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2.Class"VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3.Class"VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.
Methods
- autocovariances
signature(x = "PeriodicArmaModel", maxlag = "ANY"): ...- coerce
signature(from = "PeriodicArmaModel", to = "list"): ...- coerce
signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...- show
signature(object = "PeriodicArmaModel"): ...
Class PeriodicArmaSpec
Description
Class PeriodicArmaSpec.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicArmaSpec", pcmean, pcintercept, ...).
Slots
sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"PeriodicArmaFilter", directly.
Methods
Functions with methods for this class:
- initialize
signature(.Object = "PeriodicArmaSpec"): ...- show
signature(object = "PeriodicArmaSpec"): ...
Class PeriodicAutocorrelations
Description
Class PeriodicAutocorrelations.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicAutocorrelations", ..., data).
Slots
modelCycle:Object of class
"BasicCycle"~~data:Object of class
"Lagged"~~
Extends
Class"ModelCycleSpec", directly.Class"FlexibleLagged", directly.Class"VirtualPeriodicAutocorrelations", directly.Class"Lagged", by class "FlexibleLagged", distance 2.Class"VirtualPeriodicModel", by class "VirtualPeriodicAutocorrelations", distance 2.
Methods
- plot
signature(x = "PeriodicAutocorrelations", y = "missing"): ...
Class PeriodicAutocovariances
Description
Class PeriodicAutocovariances.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicAutocovariances", ..., data).
Slots
modelCycle:Object of class
"BasicCycle"~~data:Object of class
"Lagged"~~
Extends
Class"ModelCycleSpec", directly.Class"FlexibleLagged", directly.Class"VirtualPeriodicAutocovariances", directly.Class"Lagged", by class "FlexibleLagged", distance 2.Class"VirtualPeriodicModel", by class "VirtualPeriodicAutocovariances", distance 2.
Methods
- autocorrelations
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...- partialAutocorrelations
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
Class PeriodicBJFilter
Description
A class for filters following the Box-Jenkins sign convention
Objects from the Class
Objects can be created by calls of the formnew("PeriodicBJFilter", coef, order, ...).
Slots
coef:Object of class
"matrix"~~order:Object of class
"numeric"~~
Extends
Class"PeriodicMonicFilterSpec", directly.Class"VirtualBJFilter", directly.Class"VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2.Class"VirtualMonicFilter", by class "VirtualBJFilter", distance 2.
Methods
- filterCoef
signature(object = "PeriodicBJFilter", convention = "character"): ...- coerce
signature(from = "matrix", to = "PeriodicBJFilter"): ...- coerce
signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...- coerce
signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...- filterPoly
signature(object = "PeriodicBJFilter"): ...- filterPolyCoef
signature(object = "PeriodicBJFilter"): ...- show
signature(object = "PeriodicBJFilter"): ...
Author(s)
Georgi N. Boshnakov
See Also
filterCoef for more details on the generics
Examples
## a toy filter of order c(3, 3, 3, 3) and 4 seasonsco <- matrix(c(1, 1, 0, 2, 2, 2, 3, 0, 0, 4, 4, 4), nrow = 4, ncol = 3)## these are equivalent:bj1 <- new("PeriodicBJFilter", coef = co)bj1b <- new("PeriodicBJFilter", coef = co, order = 3)bj1c <- new("PeriodicBJFilter", coef = co, order = c(3, 3, 3, 3))identical(bj1b, bj1c) # TRUEidentical(bj1, bj1b) # FALSE but only because classbj1@order is "integer" ## a more refined spec. for the order:show( new("PeriodicBJFilter", coef = co, order = c(2, 3, 1, 3)) )## as()show( as(co, "PeriodicBJFilter") )show( as(co, "PeriodicSPFilter") )## change the sign convention:sp1 <- as(bj1, "PeriodicSPFilter")## the two parameterisations have different signs:bj1sp1## nevertheless, bj1 and sp1 represent the same filterfilterPoly(bj1)filterPoly(sp1)identical(filterPoly(bj1), filterPoly(sp1)) # TRUEfilterPolyCoef(bj1)filterPolyCoef(sp1)identical(filterPolyCoef(bj1), filterPolyCoef(sp1)) # TRUEfilterOrder(bj1)nSeasons(bj1)Class PeriodicFilterModel
Description
Class PeriodicFilterModel.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicFilterModel", pcmean, pcintercept, ...).
Slots
center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"VirtualPeriodicFilterModel", directly.Class"PeriodicArmaSpec", directly.Class"PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2.
Methods
Functions with methods for this class:
- show
signature(object = "PeriodicFilterModel"): ...
Class PeriodicIntegratedArmaSpec
Description
Class PeriodicIntegratedArmaSpec.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicIntegratedArmaSpec", ...).
Slots
pcmodel:Object of class
"PeriodicArmaModel"~~
Methods
- sigmaSq
signature(object = "PeriodicIntegratedArmaSpec"): ...- nSeasons
signature(object = "PeriodicIntegratedArmaSpec"): ...
Class PeriodicInterceptSpec
Description
Class PeriodicInterceptSpec.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicInterceptSpec", ...).
Slots
center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~sigma2:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"numeric", from data part.Class"vector", by class "numeric", distance 2.Class"index", by class "numeric", distance 2.Class"replValue", by class "numeric", distance 2.Class"numLike", by class "numeric", distance 2.Class"number", by class "numeric", distance 2.Class"atomicVector", by class "numeric", distance 2.
Methods
- sigmaSq
signature(object = "PeriodicInterceptSpec"): ...- allSeasons
signature(x = "PeriodicInterceptSpec", abb = "ANY"): ...- initialize
signature(.Object = "PeriodicInterceptSpec"): ...- nSeasons
signature(object = "PeriodicInterceptSpec"): ...- show
signature(object = "PeriodicInterceptSpec"):...
Class"PeriodicMTS"
Description
Class"PeriodicMTS" is the main class for multivariate periodictime series in package"pcts".
Objects from the Class
Objects can be created by calls of the formnew("PeriodicMTS", ...) but it is recommended to use the functionpcts in most cases.
Slots
.Data:Object of class
"matrix",the core data. Several functions can be used to extract it invarious formats, seeVec.cycle:Object of class
"BasicCycle",representing the seasonal information, seepcCycle.pcstart:Object of class
"ANY",the time of the first observation.
Extends
Class"PeriodicTimeSeries", directly.Class"matrix", from data part.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"array", by class "matrix", distance 2.Class"mMatrix", by class "matrix", distance 2.Class"optionalMatrix-class", by class "matrix", distance 2.Class"structure", by class "matrix", distance 3.Class"vector", by class "matrix", distance 4, with explicit coerce.
Methods
- $
signature(x = "PeriodicMTS"): ...- [
signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY"): ...- [
signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY"): ...- [
signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY"): ...- [
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...- [
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY"): ...- [[
signature(x = "PeriodicMTS", i = "ANY", j = "ANY"): ...- coerce
signature(from = "mts", to = "PeriodicMTS"): ...- coerce
signature(from = "PeriodicMTS", to = "ts"): ...- coerce
signature(from = "ts", to = "PeriodicMTS"): ...- coerce
signature(from = "PeriodicMTS", to = "Cyclic"): ...- coerce<-
signature(from = "PeriodicMTS", to = "Cyclic"): ...- plot
signature(x = "PeriodicMTS", y = "missing"): ...- show
signature(object = "PeriodicMTS"): ...- summary
signature(object = "PeriodicMTS"): ...- fitPM
signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...- pcApply
signature(object = "PeriodicMTS"): ...- pcMean
signature(object = "PeriodicMTS"): ...
See Also
classPeriodicTS (univariate periodic time series),
pcts (create periodic time series),
dataFranses1996 andpcts-package for examples
Examples
pcfr <- pcts(dataFranses1996)colnames(pcfr)[4] # "GermanyGNP"## extracting single time series as univariate class(pcfr[[4]]) # "PeriodicTS"identical(pcfr[[4]], pcfr$GermanyGNP ) # TRUEidentical(pcfr[[4]], pcfr[["GermanyGNP"]]) # TRUEplot(pcfr[[4]])## ... and as multivariatepcfr[4] # "PeriodicMTS"plot(pcfr[4])## extracting more than one time seriesplot(pcfr[2:4])summary(pcfr[2:4])pcfr2 <- pcfr[[2]]plot(pcfr2)Class"PeriodicMTS_ts"
Description
Class"PeriodicMTS_ts" is a periodic class holdingmultivariate"ts" objects.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicMTS_ts", x, ...).
Slots
.Data:Object of class
"vector"~~cycle:Object of class
"BasicCycle"~~pcstart:Object of class
"ANY"~~tsp:Object of class
"numeric"~~.S3Class:Object of class
"character"~~
Extends
Class"PeriodicTimeSeries", directly.Class"ts", directly.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"structure", by class "ts", distance 2.Class"oldClass", by class "ts", distance 2.Class"vector", by class "ts", distance 3, with explicit coerce.
Methods
- coerce
signature(from = "ts", to = "PeriodicMTS_ts"): ...- initialize
signature(.Object = "PeriodicMTS_ts"): ...
Class"PeriodicMTS_zooreg"
Description
Class"PeriodicMTS_zooreg" is a periodic class holdingmultivariate"zooreg" objects.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicMTS_zooreg", ...).
Slots
cycle:Object of class
"BasicCycle"~~.S3Class:Object of class
"character"~~pcstart:Object of class
"ANY"~~
Extends
Class"PeriodicTimeSeries", directly.Class"ts", directly.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"structure", by class "ts", distance 2.Class"oldClass", by class "ts", distance 2.Class"vector", by class "ts", distance 3, with explicit coerce.
Methods
No methods defined with class "PeriodicMTS_zooreg" in the signature.
Class PeriodicMaModel
Description
Class PeriodicMaModel.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicMaModel", ar, ma, sigma2, ...).
Slots
sigma2:Object of class
"numeric"~~ar:Object of class
"PeriodicArFilter"~~ma:Object of class
"PeriodicMaFilter"~~center:Object of class
"numeric"~~intercept:Object of class
"numeric"~~modelCycle:Object of class
"BasicCycle"~~
Extends
Class"PeriodicArmaModel", directly.Class"VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.Class"PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.Class"VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.Class"PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.Class"VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.Class"VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.
Methods
- show
signature(object = "PeriodicMaModel"): ...
Class PeriodicSPFilter
Description
A class for filters following the signal processing sign convention.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicSPFilter", coef, order, ...).
Slots
coef:Object of class
"matrix"~~order:Object of class
"numeric"~~
Extends
Class"PeriodicMonicFilterSpec", directly.Class"VirtualSPFilter", directly.Class"VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2.Class"VirtualMonicFilter", by class "VirtualSPFilter", distance 2.
Methods
- coerce
signature(from = "matrix", to = "PeriodicSPFilter"): ...- coerce
signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...- coerce
signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...- filterCoef
signature(object = "PeriodicSPFilter", convention = "character"): ...- filterPoly
signature(object = "PeriodicSPFilter"): ...- filterPolyCoef
signature(object = "PeriodicSPFilter"): ...- show
signature(object = "PeriodicSPFilter"): ...
Author(s)
Georgi N. Boshnakov
See Also
Examples
## see "PeriodicBJFilter-class" for examplesClass"PeriodicTS"
Description
Class"PeriodicTS" is the main class for univariate periodictime series in package"pcts".
Objects from the Class
Objects can be created from numeric vectors and objects from othertime series classes by callingpcts (recommended in mostcases).
It is possible also to use calls of the formnew("PeriodicTS", ...). This is more useful in programming.
Slots
.Data:Object of class
"numeric",the core data. Several functions can be used to extract it invarious formats, seeVec.cycle:Object of class
"BasicCycle",representing the seasonal information, seepcCycle.pcstart:Object of class
"ANY",the time of the first observation.
Extends
Class"PeriodicTimeSeries", directly.Class"numeric", from data part.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"vector", by class "numeric", distance 2.Class"index", by class "numeric", distance 2.Class"replValue", by class "numeric", distance 2.Class"numLike", by class "numeric", distance 2.Class"number", by class "numeric", distance 2.Class"atomicVector", by class "numeric", distance 2.Class"numericVector", by class "numeric", distance 2.Class"replValueSp", by class "numeric", distance 3.Class"Mnumeric", by class "numeric", distance 3.
Methods
- [
signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...- [
signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY"): ...- coerce
signature(from = "mts", to = "PeriodicTS"): ...- coerce
signature(from = "PeriodicTS", to = "ts"): ...- coerce
signature(from = "ts", to = "PeriodicTS"): ...- coerce
signature(from = "PeriodicTS", to = "Cyclic"): ...- coerce<-
signature(from = "PeriodicTS", to = "Cyclic"): ...- plot
signature(x = "PeriodicTS", y = "missing"): ...- show
signature(object = "PeriodicTS"): ...- summary
signature(object = "PeriodicTS"): ...- autocovariances
signature(x = "PeriodicTS", maxlag = "ANY"): ...- fitPM
signature(model = "PeriodicArModel", x = "PeriodicTS"): ...- pcApply
signature(object = "PeriodicTS"): ...- pcMean
signature(object = "PeriodicTS"): ...
See Also
pcts for creating"PeriodicTS" objects from rawvectors and objects from other time series classes.
PeriodicMTS for multivariate periodic timeseries.
Class"PeriodicTS_ts"
Description
Class"PeriodicTS_ts" is a periodic class holding"ts" objects.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicTS_zooreg", ...).
Objects from the Class
Objects can be created by calls of the formnew("PeriodicTS_ts", x, ...).
Slots
.Data:Object of class
"vector"~~cycle:Object of class
"BasicCycle"~~tsp:Object of class
"numeric"~~.S3Class:Object of class
"character"~~pcstart:Object of class
"ANY"~~
Extends
Class"PeriodicTimeSeries", directly.Class"ts", directly.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"structure", by class "ts", distance 2.Class"oldClass", by class "ts", distance 2.Class"vector", by class "ts", distance 3, with explicit coerce.
Methods
- coerce
signature(from = "ts", to = "PeriodicTS_ts"): ...- initialize
signature(.Object = "PeriodicTS_ts"): ...
Class"PeriodicTS_zooreg"
Description
Class"PeriodicTS_zooreg" is a periodic class holding"zooreg" objects.
Objects from the Class
Objects can be created by calls of the formnew("PeriodicTS_zooreg", ...).
Slots
cycle:Object of class
"BasicCycle"~~.S3Class:Object of class
"character"~~pcstart:Object of class
"ANY"~~
Extends
Class"PeriodicTimeSeries", directly.Class"ts", directly.Class"Cyclic", by class "PeriodicTimeSeries", distance 2.Class"structure", by class "ts", distance 2.Class"oldClass", by class "ts", distance 2.Class"vector", by class "ts", distance 3, with explicit coerce.
Methods
No methods defined with class "PeriodicTS_zooreg" in the signature.
See Also
classesPeriodicTS andPeriodicMTS
Class PeriodicTimeSeries
Description
Class PeriodicTimeSeries.
Objects from the Class
A virtual Class: No objects may be created from it.
PeriodicTimeSeries is the root class for the periodic timeseries classes in package"pcts". It can be used in signaturesfor methods that can handle objcets from any of them.
Slots
cycle:Object of class
"BasicCycle".pcstart:Object of class
"ANY".
Extends
Class"Cyclic", directly.
Methods
- as_date
signature(x = "PeriodicTimeSeries"): ...- as_datetime
signature(x = "PeriodicTimeSeries"): ...- autocorrelations
signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing"): ...- pcTest
signature(x = "PeriodicTimeSeries", nullmodel = "character"): ...- head
signature(x = "PeriodicTimeSeries"): ...- nTicks
signature(x = "PeriodicTimeSeries"): ...- pcCycle
signature(x = "PeriodicTimeSeries", type = "character"): ...- pcCycle
signature(x = "PeriodicTimeSeries", type ="missing"): ...- tail
signature(x = "PeriodicTimeSeries"): ...
See Also
classesPeriodicTS,PeriodicMTS
Class PeriodicVector
Description
Objects and methods for class PeriodicVector.
Usage
PeriodicVector(x, period = length(x))Arguments
x | the values for inidices from 1 to |
period | the period, defaults to |
Details
Ap-periodic vector,X, is such thatX_{i+pk} = X_ifor any integersi,k.
ClassPeriodicVector stores the values ofX_1,\ldots,X_pand provides indexing methods for extracting and setting itselements.
Value
an object from class"PeriodicVector"
Objects from the Class
Objects can be created by calls of the formnew("PeriodicVector", ...)or more conveniently by using"PeriodicVector()".
Slots
.Data:Object of class
"numeric"~~period:Object of class
"numeric"~~
Extends
Class"numeric", from data part.Class"vector", by class "numeric", distance 2.Class"atomicVector", by class "numeric", distance 2.Class"index", by class "numeric", distance 2.
Class"numLike", by class "numeric", distance 2.
Class"number", by class "numeric", distance 2.Class"replValue", by class "numeric", distance 2.
Methods
"PeriodicVector" methods are defined for"[" and"[<-". Arithmetic operations just inherit the recycling rulesfrom"numeric".
- [
signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY"): ...- [
signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY"): ...- [
signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY"): ...- [
signature(x = "PeriodicVector", i = "missing", j = "missing", drop = "ANY"): ...- [<-
signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY"): ...- [<-
signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY"): ...
Author(s)
Georgi N. Boshnakov
See Also
Examples
PeriodicVector(1:4, period = 4)PeriodicVector(1:4) ## samenew("PeriodicVector", 1:4, period = 4)## if period is given but x is missing, the vector is filled with NA'sPeriodicVector(period = 4)## this throws error, since length(x) != period:## PeriodicVector(1:3, period = 4)## extractx <- PeriodicVector(1:4)x[3:12]x[c(3, 7, 11, 15)]# any indices in (-Inf, Inf) workx[0]x[-3:0]## "[<-" works on the underling vectorx[1] <- 11; x## modulo indexing works also in assignments:x[5] <- 21; x## empty index returns the underlying vectorx[]## the recycling rule applies on assignmentx[] <- 9; xx[] <- 1:2; x## this gives warning, as for numeric vectors## x[] <- 8:1## compare:## x <- 1:4## x[] <- 8:1## arithmetic works as usual:2 * xx + 1:4## x + 1:3 # warning - '... a multiple ...'Class PiPeriodicArModel
Description
Class PiPeriodicArModel.
Objects from the Class
Objects can be created by calls of the formnew("PiPeriodicArModel", ...).
Slots
piorder:Object of class
"numeric"~~picoef:Object of class
"matrix"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"PiPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "PiPeriodicArmaModel", distance 2.Class"PeriodicIntegratedArmaSpec", by class "PiPeriodicArmaModel", distance 2.
Methods
- fitPM
signature(x = "ANY", model = "PiPeriodicArModel"): ...- fitPM
signature(model = "PiPeriodicArModel", x = "ANY"): ...- show
signature(object = "PiPeriodicArModel"): ...
Class PiPeriodicArmaModel
Description
Class PiPeriodicArmaModel.
Objects from the Class
Objects can be created by calls of the formnew("PiPeriodicArmaModel", ...).
Slots
piorder:Object of class
"numeric"~~picoef:Object of class
"matrix"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"VirtualPeriodicFilterModel", directly.Class"PeriodicIntegratedArmaSpec", directly.
Methods
- show
signature(object = "PiPeriodicArmaModel"): ...
Class PiPeriodicMaModel
Description
Class PiPeriodicMaModel.
Objects from the Class
Objects can be created by calls of the formnew("PiPeriodicMaModel", ...).
Slots
piorder:Object of class
"numeric"~~picoef:Object of class
"matrix"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"PiPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "PiPeriodicArmaModel", distance 2.Class"PeriodicIntegratedArmaSpec", by class "PiPeriodicArmaModel", distance 2.
Methods
No methods defined with class "PiPeriodicMaModel" in the signature.
Class SLTypeMatrix
Description
Class SLTypeMatrix is a virtual class for classes that can holdobjects with season-lag conventions.
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
No methods defined with class "SLTypeMatrix" in the signature.
Examples
showClass("SLTypeMatrix")Class SamplePeriodicAutocorrelations
Description
Class SamplePeriodicAutocorrelations.
Objects from the Class
Objects can be created by calls of the formnew("SamplePeriodicAutocorrelations", ..., data).
Slots
modelCycle:Object of class
"BasicCycle"~~data:Object of class
"Lagged"~~n:Object of class
"numeric"~~varnames:Object of class
"character"~~objectname:Object of class
"character"~~
Extends
Class"PeriodicAutocorrelations", directly.Class"Fitted", directly.Class"ModelCycleSpec", by class "PeriodicAutocorrelations", distance 2.Class"FlexibleLagged", by class "PeriodicAutocorrelations", distance 2.Class"VirtualPeriodicAutocorrelations", by class "PeriodicAutocorrelations", distance 2.Class"Lagged", by class "PeriodicAutocorrelations", distance 3.Class"VirtualPeriodicModel", by class "PeriodicAutocorrelations", distance 3.
Methods
No methods defined with class "SamplePeriodicAutocorrelations" in the signature.
Class SamplePeriodicAutocovariances
Description
Class SamplePeriodicAutocovariances.
Objects from the Class
Objects can be created by calls of the formnew("SamplePeriodicAutocovariances", ..., data).
Slots
modelCycle:Object of class
"BasicCycle"~~data:Object of class
"Lagged"~~n:Object of class
"numeric"~~varnames:Object of class
"character"~~objectname:Object of class
"character"~~
Extends
Class"PeriodicAutocovariances", directly.Class"Fitted", directly.Class"ModelCycleSpec", by class "PeriodicAutocovariances", distance 2.Class"FlexibleLagged", by class "PeriodicAutocovariances", distance 2.Class"VirtualPeriodicAutocovariances", by class "PeriodicAutocovariances", distance 2.Class"Lagged", by class "PeriodicAutocovariances", distance 3.Class"VirtualPeriodicModel", by class "PeriodicAutocovariances", distance 3.
Methods
- autocorrelations
signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
Class SiPeriodicArModel
Description
Class SiPeriodicArModel.
Objects from the Class
Objects can be created by calls of the formnew("SiPeriodicArModel", ...).
Slots
iorder:Object of class
"numeric"~~siorder:Object of class
"numeric"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"SiPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "SiPeriodicArmaModel", distance 2.Class"PeriodicIntegratedArmaSpec", by class "SiPeriodicArmaModel", distance 2.
Methods
- fitPM
signature(model = "SiPeriodicArModel", x = "ANY"): ...- show
signature(object = "SiPeriodicArModel"): ...
Class SiPeriodicArmaModel
Description
Class SiPeriodicArmaModel.
Objects from the Class
Objects can be created by calls of the formnew("SiPeriodicArmaModel", ...).
Slots
iorder:Object of class
"numeric"~~siorder:Object of class
"numeric"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"VirtualPeriodicFilterModel", directly.Class"PeriodicIntegratedArmaSpec", directly.
Methods
No methods defined with class "SiPeriodicArmaModel" in the signature.
Class SiPeriodicMaModel
Description
Class SiPeriodicMaModel.
Objects from the Class
Objects can be created by calls of the formnew("SiPeriodicMaModel", ...).
Slots
iorder:Object of class
"numeric"~~siorder:Object of class
"numeric"~~pcmodel:Object of class
"PeriodicArmaModel"~~
Extends
Class"SiPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "SiPeriodicArmaModel", distance 2.Class"PeriodicIntegratedArmaSpec", by class "SiPeriodicArmaModel", distance 2.
Methods
No methods defined with class "SiPeriodicMaModel" in the signature.
Class SimpleCycle
Description
Class SimpleCycle.
Objects from the Class
Objects can be created by calls of the formnew("SimpleCycle", nseasons, seasons, first).
In addition to number of seasons, class"SimpleCycle" holdsalso seasons' names and the index of the season to be treated as thefirst in a cycle.
Slots
seasons:Object of class
"character",the names of the seasons.nseasons:Object of class
"integer",number of seasons.cycle:Object of class
"character"~~season:Object of class
"character"~~abbreviated:Object of class
"character"~~
Extends
Class"BareCycle", directly.Class"BasicCycle", directly.
Methods
- allSeasons
signature(x = "SimpleCycle", abb = "ANY"): ...- allSeasons<-
signature(x = "SimpleCycle"): ...- coerce
signature(from = "BareCycle", to = "SimpleCycle"): ...- coerce
signature(from = "BuiltinCycle", to = "SimpleCycle"): ...- initialize
signature(.Object = "SimpleCycle"): ...- show
signature(object = "SimpleCycle"): ...- unitCycle
signature(x = "SimpleCycle"): ...- unitCycle<-
signature(x = "SimpleCycle"): ...- unitSeason
signature(x = "SimpleCycle"): ...- unitSeason<-
signature(x = "SimpleCycle"): ...
Author(s)
Georgi N. Boshnakov
See Also
pcCycle for creation of cycle objects and extraction ofcycle part of time series,
BuiltinCycle-class,SimpleCycle-class,
DayWeekCycle-class,MonthYearCycle-class,OpenCloseCycle-class,QuarterYearCycle-class,PartialCycle-class
BasicCycle-class (virtual, for use in signatures)
Examples
showClass("SimpleCycle")Class SubsetPM
Description
Class"SubsetPM" - subset PAR models with trigonometricparameterisation.
Objects from the Class
Objects can be created by calls of the formnew("SubsetPM", ...)but they are typically created by model fitting functions, see the examples.
Slots
theTS:"ANY", the time series to which the model is fitted.period:"integer", the period.order:"integer", the order.findex:"function".harmonics:"integer", Fourier harmonics to include in the model.call:"call", the call used to fit the model.other:"namedList".
Methods
- coef
signature(object = "SubsetPM"): ...- fitted
signature(object = "SubsetPM"): ...- residuals
signature(object = "SubsetPM"): ...- show
signature(object = "SubsetPM"): ...- vcov
signature(object = "SubsetPM"): ...
See Also
Examples
pcfr4 <- pcts(dataFranses1996)[[4]]x4 <- as.numeric(window(pcfr4, start = availStart(pcfr4), end = availEnd(pcfr4)))## without 'harmonics' these models are equivalenttmpfit <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE)tmpfitL <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE)## for comparisontmpfitP <- pclsdf(x4, 4, 1:2, sintercept = FALSE)## with intercepttmpfitc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = TRUE)tmpfitcn <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = structure(TRUE, merge = TRUE))tmpfitLc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE, sintercept = TRUE)coef(tmpfitc, matrix = TRUE)coef(tmpfitcn, matrix = TRUE)coef(tmpfitLc, matrix = TRUE)coef(tmpfitc)coef(tmpfitcn)coef(tmpfitLc)coef(tmpfit)coef(tmpfitL)## convert to PAR coefficients:coef(tmpfitc, type = "PAR", matrix = TRUE)coef(tmpfitcn, type = "PAR", matrix = TRUE)coef(tmpfitLc, type = "PAR", matrix = TRUE)coef(tmpfitL, type = "PAR", matrix = TRUE)predict(tmpfitc, n.ahead = 4)predict(tmpfitcn, n.ahead = 4)sqrt(diag((vcov(tmpfitL))))e <- residuals(tmpfitL)fi <- fitted(tmpfitL)Core data of periodic time series
Description
Extract the core data from a periodic time series as a vector, matrixor array.
Usage
Vec(x, ...)tsMatrix(x, ...)tsVector(x, ...)tsVec(x, ...)pcMatrix(x, ...)pcArray(x, ndim = 3, ...)pctsArray(x, ndim = 3, ...)Arguments
x | an object. |
... | further arguments for methods. |
ndim | currently not used. |
Details
These functions give the core data in various common forms.
The data values can be extracted as a vector from a periodic timeseries object, sayx, withas.vector(x) oras(x, "vector"). For multivariate time series the vector returned byas.vector(x) (oras(x, "vector")) is equivalent toas.vector(as.matrix(x)).
Similarly,as.matrix() andas(x, "matrix")extract the data as a matrix containing one column per variable.
Vec() is likeas.vector() but the result is a matrixwith one column (column vector). The default does literally this.Thus both,Vec() andas.vector(), implement theVec operation from matrix calculus but the latter returns theresult as a vector, not matrix.
The most common representation of data in statistics is matrix-likewith one column per variable. The descriptions of algorithms formultivariate time series however usually define the vector ofobservations at a given time to be a column vector. In particular,implementations of the Kalman filter often require precisely thisarrangement. In that case the data matrix is the transposed of themore common one and the vectorising operation stacks the observations,not the variables.
The functionstsMatrix(),tsVector() andtsVec()provide the analogues ofas.vector(),as.matrix() andVec() for the “transposed” arrangement.
These functions may look redundant since they are simple combinationsof the above and traspose operations. Having functions makes for morereadable programming. They may be more efficient, as well, for exampleif the underlying time series class stores the data in the transposedformat.
pcMatrix() andpcArray() also give the coredata. Effectively, they give an additional dimension to theseasons. The season becomes the first dimension since for columnoriented data the season changes fastest.pcMatrix is mostsuitable for univariate time series,pcArray() formultivariate. Note thatpcArray() easily extends to multipleperiodicities although currently (2019-04-19) there are no methodsthat exploit this.
For univariate time series, in the matrix returned bypcMatrix() each row represents the data for one season and eachcolumn for one cycle. For multivariate time series, the matrices foreach variable are put next to each other.
pcArray() returns the data as an array, whose last dimensioncorresponds to variables. In the default case the array is3-dimensonal with dimensions (season, year, variable).
pctsArray() is a variant ofpcArray() corresponding tothe arrangement oftsMatrix(). The ordering of the dimensionshere is (variable, season, cycle).
Value
vector, matrix or array, as indicated by the name of the function anddescribed in section ‘Details’.
Author(s)
Georgi N. Boshnakov
Examples
## window to make number of years different from number of monthsap <- pcts(window(AirPassengers, start = c(1956, 1)))class( as.vector(ap) )class( as(ap, "vector") )dim( as.matrix(ap) )dim( as(ap, "matrix") )dim( tsMatrix(ap) )class( tsVector(ap) ) dim( tsVec(ap) ) dim( pcMatrix(ap) )dim( pcArray(ap) )dim( pctsArray(ap) )dfr <- pcts(dataFranses1996)dim(dfr) # c(148, 19)nSeasons(dfr) # 4length(as.vector(dfr))all.equal(as.vector(dfr)[1:148], as.matrix(dfr)[ , 1]) # TRUEall.equal(tsVector(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUEdim( as.matrix(dfr) ) # c(148, 19)dim( tsMatrix(dfr) ) # c(19, 148)all.equal(tsMatrix(dfr)[ , 1], as.matrix(dfr)[1, ]) # TRUEdim( Vec(dfr) ) dim( tsVec(dfr) ) all.equal(tsVec(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUEdim( pcMatrix(dfr) ) # c(4, 703), one row for each seasondim( pcArray(dfr) ) # c(4, 37, 19), note: 703 == 37*19 dim( pctsArray(dfr) ) # c(19, 4, 37), note: 703 == 37*19~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
Objects can be created by calls of the formnew("VirtualPeriodicArModel", ...).
Extends
Class"VirtualPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2.Class"VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2.Class"VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3.Class"VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.
Methods
No methods defined with class "VirtualPeriodicArModel" in the signature.
Class VirtualPeriodicArmaModel
Description
Class VirtualPeriodicArmaModel.
Objects from the Class
Objects can be created by calls of the formnew("VirtualPeriodicArmaModel", ...).
Extends
Class"VirtualPeriodicFilterModel", directly.Class"VirtualPeriodicStationaryModel", directly.Class"VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicStationaryModel", distance 2.Class"VirtualPeriodicMeanModel", by class "VirtualPeriodicStationaryModel", distance 2.
Methods
- PeriodicArModel
signature(object = "VirtualPeriodicArmaModel"): ...
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Extends
Class"VirtualPeriodicModel", directly.
Methods
No methods defined with class "VirtualPeriodicAutocorrelations" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
- [
signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "missing", drop = "ANY"): ...- [
signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "numeric", drop = "ANY"): ...- [
signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "missing", drop = "ANY"): ...- [
signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "numeric", drop = "ANY"): ...- maxLag
signature(object = "VirtualPeriodicAutocovarianceModel"): ...- autocorrelations
signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "missing", lag_0 = "ANY"): ...- autocorrelations
signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "numeric", lag_0 = "ANY"): ...
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Extends
Class"VirtualPeriodicModel", directly.
Methods
- autocorrelations
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...- autocovariances
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY"): ...- backwardPartialCoefficients
signature(x = "VirtualPeriodicAutocovariances"): ...- backwardPartialVariances
signature(x = "VirtualPeriodicAutocovariances"): ...- partialAutocorrelations
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "ANY"): ...- partialAutocovariances
signature(x = "VirtualPeriodicAutocovariances"): ...- partialCoefficients
signature(x = "VirtualPeriodicAutocovariances"): ...- partialVariances
signature(x = "VirtualPeriodicAutocovariances"): ...- pc.bU
signature(x = "VirtualPeriodicAutocovariances"): ...- pc.fL
signature(x = "VirtualPeriodicAutocovariances"): ...- pc.phis2
signature(x = "VirtualPeriodicAutocovariances"): ...
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
No methods defined with class "VirtualPeriodicFilterModel" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
Objects can be created by calls of the formnew("VirtualPeriodicMaModel", ...).
Extends
Class"VirtualPeriodicArmaModel", directly.Class"VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2.Class"VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2.Class"VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3.Class"VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.
Methods
No methods defined with class "VirtualPeriodicMaModel" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
No methods defined with class "VirtualPeriodicMeanModel" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
- allSeasons
signature(x = "VirtualPeriodicModel", abb = "ANY"): ...- nSeasons
signature(object = "VirtualPeriodicModel"): ...- seqSeasons
signature(x = "VirtualPeriodicModel"): ...- unitCycle
signature(x = "VirtualPeriodicModel"): ...- unitSeason
signature(x = "VirtualPeriodicModel"): ...
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
A virtual Class: No objects may be created from it.
Methods
No methods defined with class "VirtualPeriodicMonicFilter" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
Objects can be created by calls of the formnew("VirtualPeriodicStationaryModel", ...).
Extends
Class"VirtualPeriodicAutocovarianceModel", directly.Class"VirtualPeriodicMeanModel", directly.
Methods
No methods defined with class "VirtualPeriodicStationaryModel" in the signature.
~~ Dummy title ~~
Description
~~ Dummy description ~~
Objects from the Class
Objects can be created by calls of the formnew("VirtualPeriodicWhiteNoiseModel", ...).
Extends
Class"VirtualPeriodicStationaryModel", directly.Class"VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicStationaryModel", distance 2.Class"VirtualPeriodicMeanModel", by class "VirtualPeriodicStationaryModel", distance 2.
Methods
No methods defined with class "VirtualPeriodicWhiteNoiseModel" in the signature.
Index assignments for objects from classes in package pcts
Description
Index assignments for objects from classes in package pcts.
Methods
signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY")signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY")signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")signature(x = "PeriodicAutocovarianceModel", i = "ANY", j = "ANY", value = "ANY")
Author(s)
Georgi N. Boshnakov
Indexing of objects from classes in package pcts
Description
Indexing of objects from classes in package pcts.
Methods
signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY")signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY")signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY")signature(x = "PeriodicVector", i = "missing", j = "missing", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "missing", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "numeric", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "missing", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "numeric", drop = "ANY")signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY")signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY")signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing", drop = "ANY")signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing", drop = "ANY")
Author(s)
Georgi N. Boshnakov
Methods for function`[[` in package 'pcts'
Description
Methods for function`[[` in package 'pcts'.
Methods
signature(x = "PeriodicMTS", i = "ANY", j = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "ANY")
Get names of seasons
Description
Functions and methods fo get names of seasons and related quantitiesfor objects from the cycle, periodic time series classes and otherobjects for which the concepts are defined.
Usage
unitSeason(x)unitCycle(x)seqSeasons(x)allSeasons(x, abb = FALSE, prefix = "S", ...)unitSeason ( x, ... ) <- valueunitCycle ( x, ... ) <- valueallSeasons ( x, abb, ... ) <- value## S4 replacement method for signature 'SimpleCycle'allSeasons(x, abb, prefix, ...) <- value## S4 replacement method for signature 'Cyclic'allSeasons(x, abb = FALSE, ...) <- valueArguments
x | a cycle, time series or other object for which the concept ofseasons is defined. |
abb | if |
prefix | use this prefix for automatically generated names of seasons. |
... | further arguments for methods. |
value | a character string |
Details
The cycle classes, i.e. classes inheriting from classBasicCycle, provide common functionality. Inparticular, they guarantee that the functions described in this topicare available. These functions work also for the periodic time seriesclasses and may be defined for other classes where they make sense.
Methods
Methods forallSeasons():
signature(x = "BasicCycle", abb = "ANY")signature(x = "DayWeekCycle", abb = "logical")signature(x = "DayWeekCycle", abb = "missing")signature(x = "MonthYearCycle", abb = "logical")signature(x = "MonthYearCycle", abb = "missing")signature(x = "OpenCloseCycle", abb = "logical")signature(x = "OpenCloseCycle", abb = "missing")signature(x = "QuarterYearCycle", abb = "logical")signature(x = "QuarterYearCycle", abb = "missing")signature(x = "SimpleCycle", abb = "ANY")signature(x = "Cyclic", abb = "ANY")signature(x = "Every30MinutesCycle", abb = "logical")signature(x = "Every30MinutesCycle", abb = "missing")signature(x = "VirtualPeriodicModel", abb = "ANY")
Author(s)
Georgi N. Boshnakov
Examples
opcycle <- new("OpenCloseCycle")## convert to SimpleCycle to change some namessiopcycle <- as(opcycle, "SimpleCycle")## siopcycle inherits names from opcycleunitSeason(siopcycle) # "Season"unitCycle(siopcycle) # "Cycle"allSeasons(siopcycle) # "Open" "Close"allSeasons(siopcycle, abb = TRUE) # "O" "C"allSeasons(siopcycle) <- c("Day", "Night")allSeasons(siopcycle) # now: "Day" "Night"## change also abbreviationsallSeasons(siopcycle, abb = TRUE) <- c("D", "N")allSeasons(siopcycle, abb = TRUE) # now: "D" "N"seasons <- new("SimpleCycle", 4)unitSeason(seasons) # "Season"unitCycle(seasons) # "Cycle"allSeasons(seasons)allSeasons(seasons, abb = TRUE) unitCycle(seasons) <- "Year"unitCycle(seasons)allSeasons(seasons) <- c("Winter", "Spring", "Summer", "Autumn")allSeasons(seasons)allSeasons(seasons, abb = TRUE) <- c("Win", "Spr", "Sum", "Aut")allSeasons(seasons, abb = TRUE)## change autumn to FallallSeasons(seasons)[4] <- "Fall"allSeasons(seasons, abb = TRUE)[4] <- "Fal"allSeasons(seasons)allSeasons(seasons, abb = TRUE)## indexing of cycle objects is equivalent to allSeasons.seasons[]seasons[ , abb = TRUE]seasons[4] <- "Herbst"seasonsunitCycle(seasons) <- "Jahre"unitCycle(seasons)unitSeason(seasons) <- "Jahreszeit"seasons[] <- c("Winter", "Frueling", "Sommer", "Herbst")seasons[ , abb = TRUE] <- c("W", "F", "S", "H")seasons[]seasonsReplace methods for as_date in package pcts
Description
Replace methods for as_date in package pcts.
Methods
signature(x = "PeriodicTimeSeries")signature(x = "ANY")signature(x = "character")signature(x = "Cyclic")signature(x = "numeric")signature(x = "POSIXt")
Methods for as_datetime in package pcts
Description
Methods for as_datetime in package pcts.
Methods
signature(x = "PeriodicTimeSeries")
Compute autocorrelations and periodic autocorrelations
Description
Methods for computation of autocorrelations and periodicautocorrelations.
Methods
signature(x = "numeric", maxlag = "ANY", lag_0 = "missing")signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing")signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "ANY", lag_0 = "missing")
See Also
autocorrelations in packagesarimafor further details.
autocovariances for autocovariances;
Examples
## periodic ts object => peridic acfautocorrelations(pcts(AirPassengers), maxlag = 10)## for "ts" or "numeric" objects the default is non-periodic acfautocorrelations(AirPassengers, maxlag = 10) autocorrelations(as.numeric(AirPassengers))## argument 'nseasons' forces periodic acfautocorrelations(AirPassengers, maxlag = 10, nseasons = 12)autocorrelations(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)Compute autocovariances and periodic autocovariances
Description
Methods for the generic functionautocovariances(), whichcomputes autocovariances meaningful for the first argument. Forobjects representing time series, it computes sample autocovariances(univariate, multivariate, periodic, as appropriate). For objectsrepresenting models, it computes the relevant theoreticalautocovariances.
Methods
signature(x = "matrix", maxlag = "ANY")signature(x = "numeric", maxlag = "ANY")signature(x = "PeriodicArmaModel", maxlag = "ANY")signature(x = "PeriodicArModel", maxlag = "ANY")signature(x = "PeriodicAutocovarianceModel", maxlag = "ANY")signature(x = "PeriodicTS", maxlag = "ANY")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY")If
maxlagis missing or equal tomaxLag(x),xis returned unchanged. Otherwise the number of available lags isadjusted tomaxlag.
See Also
autocovariances in packagesarimafor further details.
autocorrelations for autocorrelations;
Examples
## periodic ts object => peridic acvfautocovariances(pcts(AirPassengers), maxlag = 10)## for "ts" or "numeric" objects the default is non-periodic acvfautocovariances(AirPassengers, maxlag = 10) autocovariances(as.numeric(AirPassengers))## argument 'nseasons' forces periodic acvfautocovariances(AirPassengers, maxlag = 10, nseasons = 12)autocovariances(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)Time of first or last non-NA value
Description
Time of first or last non-NA value.
Usage
availStart(x, any = TRUE)availEnd(x, any = TRUE)Arguments
x | a time series or similar object |
any | logical flag for multivariate objects. The default |
Details
The time is given as a cycle-season pair.
Argumentany is meaningful only for multivariate objects. Itsname is short for"the first/last index for which any of the values (ie at least one) is non-NA".any = FALSE is taken to mean that the index is the first/lastfor which all values are non-NA.
The functions can be used together withwindows to trimNA's from the beginning and/or end of the data. As analternative we provide also methods for periodic time series methodsforzoo:na.trim, see the examples below.
Value
numeric, length 2
See Also
Examples
tipi <- pcts(dataFranses1996[ , "USTotalIPI"])start(tipi)end(tipi)head(tipi)tail(tipi)tipi <- window(tipi, start = availStart(tipi), end = availEnd(tipi))start(tipi)end(tipi)plot(tipi)pcfr <- pcts(dataFranses1996)pcfr2to4 <- pcfr[2:4]head(pcfr2to4)tail(pcfr2to4)## time of first and last data, can be NA'sstart(pcfr2to4) # 1955 Q1end(pcfr2to4) # 1991 Q4## time of first nonNA:availStart(pcfr[[2]]) # 1960 Q1availStart(pcfr2to4) # 1960 Q1## time of last nonNA:availEnd(pcfr[[2]]) # 1991 Q4availEnd(pcfr[[3]]) # 1987 Q4availEnd(pcfr[[4]]) # 1990 Q4## but at least one of them is available for 1991 Q4, so:availEnd(pcfr2to4) # 1991 Q4## this requests the time of the last full record:availEnd(pcfr2to4, any = FALSE) # 1987 Q4pcfr2to4a <- window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4))head(pcfr2to4a)tail(pcfr2to4a, 20)## trim NA's from both ends, up to the firsxst/last full record:pcfr2to4b <- window(pcfr2to4, start = availStart(pcfr2to4, FALSE), end = availEnd(pcfr2to4, FALSE))## TODO: need a better example here since the first non-NA value for all## ts in pcfr2to4 is at the same## alternatively, use na.trim(), the default for is.na is "any"pcpres <- window(pcts(presidents), end = c(1972, 4))availStart(pcpres) # 1945 2availEnd(pcpres) # 1972 2both <- na.trim(pcpres) # same as "both"identical(na.trim(pcpres), both) # TRUEhead(both, 7)tail(both)head(na.trim(pcpres, "left"), 7)tail(na.trim(pcpres, "right"))cguk <- pcfr[c("CanadaUnemployment", "GermanyGNP", "UKTotalInvestment")]availStart(cguk)availStart(cguk, TRUE) # sameavailStart(cguk, FALSE)availEnd(cguk)availEnd(cguk, TRUE) # sameavailEnd(cguk, FALSE)na.trim(cguk)head( na.trim(cguk, sides = "left") )tail( na.trim(cguk, sides = "right") )head( na.trim(cguk, sides = "left", is.na = "all") )tail( na.trim(cguk, sides = "right", is.na = "all") )Compute periodic backward partial coefficients
Description
Methods for computation of periodic backward partial coefficients.
Methods
signature(x = "VirtualPeriodicAutocovariances")
Compute periodic backward partial variances
Description
Compute periodic backward partial variances.
Methods
signature(x = "VirtualPeriodicAutocovariances")
Example data from Franses (1996)
Description
A multivariate time series containing the data usedin examples by Franses (1996).
Usage
data("dataFranses1996")Format
A multivariate quarterly time series.
Details
Each column is a quarterly time series. The time series start and endat different times, soNA's are used to align them in a singlemultivariate time series. Detailed account of the sources of the datais given by@FransesB1; Data Appendix), p. 214.
year(column 1)
The time formatted as
yyyy.Q, whereyyyyis the yearandQis the quarter (one of 1, 2, 3 or 4.). This columnwas part of the original data but is not really needed here sincethe time series object contains the time information.USTotalIPI(column 2)
Total Industrial Production Index for the United States (1985 =100), 1960.1–1991.4.
CanadaUnemployment(column 3)
Unemployment in Canada, measured in 1000 persons, 1960.1 - 1987.4.
GermanyGNP(column 4)
Real GNP in Germany, 1960.1 - 1990.4 .
UKTotalInvestment(column 5)
Real Total Investment in the United Kindom, 1955.1 - 1988.4.
SA_USTotalIPI(column 6)Seasonally adjusted
USTotalIPI.SA_CanadaUnemployment(column 7)
Seasonally adjusted
CanadaUnemployment.SA_GermanyGNP(column 8)
Seasonally adjusted
GermanyGNP.UKGDP(column 9)
United Kingdom gross domestic product (at 1985 prices),1955.1–1988.4.
UKTotalConsumption(column 10)
United Kingdom total consumption (at 1985 prices),1955.1–1988.4.
UKNondurablesConsumption(column 11)
United Kindom nondurables consumption (at 1985 prices), 1955.1–1988.4.
UKExport(column 12)
United Kindom exports of goods and services (at 1985 prices),1955.1–1988.4.
UKImport(column 13)
United Kindom imports of goods and services (at 1985 prices),1955.1–1988.4.
UKPublicInvestment(column 14)
United Kindom public investment (at 1985 prices), 1962.1–1988.4.
UKWorkforce(column 15)
United Kindom workforce (consisting of workforce in employment andunemployment), 1955.1–1988.4.
SwedenNondurablesConsumption(column 16)
Real per capita non-durables consumption in Sweden (measured inlogs), 1963.1–1988.1.
SwedenDisposableIncome(column 17)
Real per capita disposable income in Sweden (measured in logs),1963.1–1988.1.
SA_SwedenNondurablesConsumption(column 18)
Seasonally adjusted
SwedenNondurablesConsumptionwithCensus X-11 method, 1964.1–1988.1. (Using the approximate linearCensus X-11 filter given in Table 4.1, p. 52 inFranses (1996) and generating the forecastsand backcasts as described in Ooms (1994)).SA_SwedenDisposableIncome(column 19)
Seasonally adjusted
SwedenDisposableIncomewith Census X-11method, 1964.1–1988.1. (Using the same method as above.)
More details on the individual time series are given byFranses (1996).
Note
Most of the time series indataFranses1996 are available asseparate datasets in package ‘partsm’. The numbers should be the samebut note that, at the time of writing this, not all datasets therecarry complete time information.
Source
The data were downloaded fromhttp://people.few.eur.nl/franses/research/data/data1.txt,but this link is now broken.
References
Franses PH (1996).Periodicity and Stochastic Trends In Economic Time Series.Oxford University Press Inc., New York.
See Also
Fraser2017,four_stocks_since2016_01_01
Examples
data(dataFranses1996)class(dataFranses1996)colnames(dataFranses1996)dim(dataFranses1996) # c(148, 19)plot(dataFranses1996[ , 2:11])tipi <- dataFranses1996[ , "USTotalIPI"]plot(tipi)## convert to PeriodicTS and remove NA's at the start and endpctipi <- pcts(tipi)pctipi <- window(pctipi, start = availStart(pctipi), end = availEnd(pctipi))plot(pctipi)## convert the whole dataset to class "PeriodicMTS"pcfr <- pcts(dataFranses1996)colnames(pcfr)[2:3] # "USTotalIPI" "CanadaUnemployment"## subset as "PeriodicMTS"pcfr2to3 <- pcfr[2:3]plot(pcfr2to3)## "[" "PeriodicMTS" even with length one arg.pcfr2to2 <- pcfr[2]pcfr2to2a <- pcfr["USTotalIPI"] # same## use "[[" or $ to get "PeriodicTS"pcfr2 <- pcfr[[2]]pcfr2a <- pcfr[["USTotalIPI"]] # samepcfr2b <- pcfr$USTotalIPI # sameidentical(pcfr2, pcfr2a) # TRUEidentical(pcfr2, pcfr2b) # TRUEcycle(pcfr)frequency(pcfr)Replace methods for date in package pcts
Description
Replace methods for date in package pcts.
Methods
signature(x = "BasicCycle")signature(x = "Cyclic")
An example PAR autocorrelation function
Description
ex1 is the autocorrelation function used in the reference as anexample when the solution of the periodic Yule-Walker system gives aninvalid PAR model. This can happen only if Lambert-Lacroix'scondition on the PAR order is not satisfied, seepdSafeParOrder.
Format
A function of two arguments
Source
See pp. 429–430 of the reference.
References
Lambert-Lacroix S (2005).“ Extension of autocovariance coefficients sequence for periodically correlatedprocesses.”Journal of Time Series Analysis,26(6), pp. 423-435.
See Also
Examples
data(ex1f)## compute the first few autocorrelationspc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt")## Fir a PAR(0,2) modelres0p2 <- alg1(pc3[],c(0,2))## model is invalid since a partial autocorrelation is larger than one:res0p2$be## Find a modified order:pdSafeParOrder(c(0,2)) # PAR(1,2)## now the parcor's are fine:res1p2 <- alg1(pc3[],c(1,2))res1p2$beGet the coefficients of a periodic filter
Description
Get the coefficients of a periodic filter.
Details
filterCoef is a generic function to extract the coefficients ofperiodic filters. Argumentconvention can be used to force aparticular convention for the signs. The description here is for themethods defined in this package.
Ifconvention is missing, the coefficient matrix is returned asstored in the object. Otherwise, ifconvention is one of thestrings"BJ","--" or"-", the coefficientsreturned have the opposite sign of those in the auxilliary polynomial(Box-Jenkins' convention). Ifconvention is one of"SP","++" or"+", the coefficients are as in the auxilliarypolynomial (convention used in signal processing).
Value
a matrix
Methods
signature(object = "PeriodicBJFilter", convention = "character")signature(object = "PeriodicSPFilter", convention = "character")
See Also
filterCoef for further details;
PeriodicBJFilter for examples
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Description
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Methods
signature(object = "PeriodicBJFilter")signature(object = "PeriodicSPFilter")
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Description
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Methods
signature(object = "PeriodicBJFilter")signature(object = "PeriodicSPFilter")
Fit periodic time series models
Description
Generic function with methods for fitting periodic time series models.
Usage
fitPM( model, x, ...)Arguments
x | the time series. |
model | a periodic model, see Details. |
... | further arguments to be passed on to individual methods. |
Details
This is a generic function.
model provides the specification of the model. In particular,the class ofmodel determines what model is fitted. Specificvalues of the parameters are generally ignored by non-iterativemethods but some methods can handle more detailed specifications, seethe individual methods.
Value
the fitted model,typically an object of classclass(model)
Methods
signature(model = "ANY", x = "ANY")This is the default method. It simply exits with an error messagestating that
fitPMdoes not have a method for the modelspecified bymodel.signature(model = "numeric", x = "ANY")Fits a PAR model to
x.modelshould be a vector ofnon-negative integers giving the PAR order. The length of this vectoris taken to be the number of seasons.This is a convenience method. It constructs a PAR model and callls themethod for
model = "PeriodicArModel".signature(model = "PeriodicArModel", x = "ANY")Fits a PAR model.
signature(model = "mcSpec", x = "ANY")Fits a periodic model according to the specification given by
model.Currently this method uses
mC.ssto set up theoptimisation environment and then calls one of the optimisationfunctions in that environment as specified by argumentoptim.method, see below.Additional arguments may be specified to control the optimisation.
Argument
initcan be used to give initial values. It ispassed on tomC.ss(and so has the format required by it).optim.methodis the name of an optimisation function in theenvironment returned bymC.ss. The default isoptim.method = "minim", which is based on the standardR functionoptim. Alternatives are "minimBB" or "minimBBLU". All thisneeds to be documented but seemC.ssandxx.ssfordetails.Further arguments are passed on to the optimisation method. Atypical argument supported by most optimisation functions is
control.signature(model = "PiPeriodicArModel", x = "ANY")Fits a periodically integrated PAR model using the parameters of
modelas initial values. Callspclspiarto do theactual work.signature(model = "SiPeriodicArModel", x = "ANY")Fits a seasonally integrated PAR model.
signature(model = "PeriodicArModel", x = "PeriodicMTS")signature(model = "PeriodicArModel", x = "PeriodicTS")
Author(s)
Georgi N. Boshnakov
References
(todo: to be completed properly later)
Hipel KW, McLeod AI (1994).Time series modelling of water resources and environmental systems, Developments in water science; 45.London; Amsterdam: Elsevier.
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
Examples
## newm1 <- list(phi = matrix(1:12, nrow=4), p=rep(3,4), period=4, si2 = rep(1,4))## new_pfm1 <- PeriodicFilterModel(newm1, intercept=0)## generate some data;set.seed(1234)simts1 <- pcts(rnorm(1024), nseasons = 4)fitPM(c(3,3,3,3), simts1)fitPM(3, simts1)## the fit on the underlying data is equivalent.fitPM(c(3,3,3,3), as.numeric(simts1))## equivalently, use a PAR(3,3,3,3) model for argument 'model'## here the coefficients of pfm1 are ignored, since the estimation is linear.pfm1 <- PeriodicArModel(matrix(1:12, nrow = 4), order = rep(3,4), sigma2 = 1)pfm1## these give same results as abovefitPM(pfm1, simts1)fitPM(pfm1, as.numeric(simts1))fitPM(c(1,1,1,1), simts1)fitPM(c(3,2,2,1), simts1)fitPM(c(3,2,2,2), simts1)pdSafeParOrder(c(3,2,2,1))pdSafeParOrder(rev(c(3,2,2,1)))x <- arima.sim(list(ar = 0.9), n = 960)pcx <- pcts(x, nseasons = 4)mx <- matrix(x, nrow = 4)##pc.acf(mx)##pc.acf(mx, maxlag=10)## TODO: avoid the warning when length ot the time series is not multipleautocovariances(t(mx), maxlag = 6, nseasons = 4)autocovariances(t(mx))##It is an error to have more columns than rows.## autocovariances(mx, maxlag = 6, nseasons = 4)## autocovariances(mx)num2pcpar(mx, c(1,1,1,1), period = 4)num2pcpar(mx, c(3,3,3,3), period = 4)sipfm1 <- new("SiPeriodicArModel", iorder = 1, siorder = 1, pcmodel = pfm1)sipfm1fitPM(sipfm1, mx)pfm1## experiments and testingfit1 <- fitPM(c(3,3,3,3), simts1)fit1_mf <- new("MultiFilter", coef = fit1@ar@coef)vs <- mcompanion::mf_VSform(fit1_mf, form = "I")tmp <- mcompanion::VAR2pcfilter(vs$Phi[ , -4], Phi0inv = vs$Phi0inv, D = fit1@sigma2, what = "")names(tmp) # "pcfilter" "var" "Uform" tmp$varzapsmall(tmp$pcfilter)fit1@ar@coefall.equal(tmp$pcfilter[ , 1:3], fit1@ar@coef, check.attributes = FALSE) # TRUEtmp$Uformfit1@sigma2## both give the matrix Sigma for the "I" formidentical( vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv) , tmp$Uform$U0inv %*% diag(tmp$Uform$Sigma) %*% t(tmp$Uform$U0inv)) # TRUE## no, this is a different matrixvar1_mat <- cbind(vs$Phi0, # identity matrix - vs$Phi) # drop trailing zero columns?var1_mat <- mcompanion::mCompanion(var1_mat)var1_Sigma <- vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv)abs(eigen(diag(nrow(var1_mat)) - var1_mat)$values)Fit a subset trigonometric PAR model
Description
Fit a subset PAR model with trigonometric parameterisation.
Usage
fit_trigPAR_optim(x, order, nseasons, seasonof1st = 1, maxiter = 200, harmonics = NULL, sintercept = FALSE, tol = 1e-07, type = c("vecbyrow", "bylag"), verbose = TRUE)Arguments
x | time series. |
order | order, an integer number. |
nseasons | number of seasons, an integer number. |
seasonof1st | season of the first observation. |
maxiter | max number of iterations. |
harmonics | the harmonics to include in the model, vector of non-negativeintegers. |
sintercept | if |
tol | when to stop the iterations. |
type | type of parameterisation, currently one of |
verbose | if |
Details
Fits a subset PAR model using trigonometric parameterisation,i.e. Fourier series for the periodic coefficients written in terms ofsines and cosines.
If argumenttype isbylag, the parameters for each lagare parameterised independently from other lags. IfsinterceptisTRUE, it has its own trigonometric representation.
If argumenttype isvecbyrow (“Vec operation byrow”), the PAR parameters are stacked in a vector with all parametersfor the first season, followed by all parameters for the second, andso on. The trigonometric parameterisation for this vector is used.So the fundamental frequency is1/(nseasons * order).Ifsintercept isTRUE whentype = vecbyrow, thenthen the intercept for eaach season is put before the PAR parametersand the fundamental frequency becomes1/(nseasons * (order + 1). Putting together the intercepts and the PAR parameters may not be veryuseful for parsimonious trigonometric parameterisation, so to have aseparate set of coefficients for the intercepts setattribute"merge" ofsintercept toFALSE.
Value
an object from classSubsetPM
Note
This function may change.
Author(s)
Georgi N. Boshnakov
Examples
## see examples for class "SubsetPM"Data for four stocks since 2016-01-01
Description
Data for four stocks since 2016-01-01.
Usage
data("four_stocks_since2016_01_01")Format
A list with components "DELL","MSFT", "INTC", "IBM".Each component is a time series from class"xts" "zoo".
Details
Stock market data for Dell, Microsoft, Intel and IBM, from 2016-01-01to 2020-04-17. The Dell data start from 2016-08-17. All data weredownloaded from Yahoo Finance on 2020-04-18.
Source
https://finance.yahoo.com/
See Also
Examples
data(four_stocks_since2016_01_01)DELL <- four_stocks_since2016_01_01$DELLhead(DELL)tail(DELL)dell <- pcts(DELL)head(as_datetime(dell))head(Pctime(dell))## Weekends are totally absent from the data,## so a Monday-Friday sub-cycle is created:nSeasons(dell)dell@cycle## there are some NA's in the data, due to Bank holidaysPctime(c(2624, 5), pcCycle(dell)) # "W2624 Fri"as_datetime(Pctime(c(2624, 5), pcCycle(dell))) # "2020-04-10 UTC"## dell["2020-04-10 UTC"]head(cycle(dell))tail(Pctime(dell))tail(as.Date(Pctime(dell)))Methods for function head() in package pcts
Description
Methods for function head() in package pcts.
Methods
signature(x = "PeriodicTimeSeries")
Create environment for mc-fitting
Description
Creates an environment for mc-fitting. These functions are transitory,hence the strange names.
Usage
mC.ss(spec, ...)xx.ss(period, type.eigval, n.root, eigabs, eigsign, co_r, co_arg, init = NULL, len.block = NULL, mo.col, generators = NULL)Arguments
spec | a model, an object of class mcSpec. |
... | further arguments to be passed on to |
period | the number of seasons. |
type.eigval | types of the eigenvalues, a character vector withelements "r" or "cp", see Details. |
n.root | number of roots. Currently the dimension of the matrixis set to this. |
eigabs | The absolute values/moduli of the eigenvalues, numeric vector. |
eigsign | The signs/moduli of the eigenvalues. |
co_r | similar to |
co_arg | similar to |
init | initial values, see Details. |
len.block | lengths of Jordan blocks. |
mo.col | last non-zero column in the top of the matrix. |
generators | ~~ TODO: describe this argument. ~~ |
Details
mC.ss takes the specification of the model as an object ofclass mcSpec and callsxx.ss.
Basically, the value returned by these functions is an extendedmodel specification together with an environment which can be used forfitting the model, exploring the results and trying various things.This may be used for getting better understanding of the model and theoptimisation routines.
The result of both functions is a list, containing several functionsand an environment. The environment (elementenv) is the mostimportant element since it allows access to everything in the modelenvironment. The function elements of the list are simply aconvenience.
Several functions inenv are available for fitting themodel. Currently these areminim,minimBB andminimBBlu. The first argument of all these functions is a timeseries to which the model is to be fitted. By default, a conditionallikelihood is being optimised. To base the optimisation on conditionalsum of squares, set argumentCONDLIK to FALSE. The remainingarguments in a call to any of the above functions are passed on to thecorresponding optimisation routine (whose help page should beconsulted for details).
minim uses the coreR functionoptim.minimBB andminimBBlu useBBoptim from packageBB. They result is a list, as returned by the correspondingoptimisation function with the optimal parameters in elementpar. The elements of this vector are named to help somewhat inits interpretation but complete information about the fitted model canbe obtained from the environment.
Firstly, at the end of the optimisation, the optimal parameters andother information are stored inenv. If the same call (maybewith modified instructions for the optimisation) is repeated, theseparameters will be used as initial values for a new optimisationrun. This may be useful, for example, if the previous run didn'tconverge.
Secondly, properties of the fitted model and more usefulrepresentations can be obtained using functions in the environment orthe convinience functions in the list returned byxx.ss.
optparam2mcparam converts a vector of parameters into themore familiar filter representation, where the i-th row contains thecoefficients for the i-th season. This function takes one argument thevector of parameters, e.g. the one returned by the fittingfunctions. It updates a number of variables inenv, computesthe filter representation of the model and stores it inwrkmodel. It returns NULL.This function may be used for exploratory purposes or to set newvalues for the parameters, e.g. to be used as starting values for anew optimisation run.
mcparam2optparam does the opposite. It converts the currentmodel inenv to a vector of parameter. This function does nothave arguments.
mclik computes the value of the conditional likelihood forgiven parameters. Its first argument is a time series, the second is avector of parameters and the third is a vector of innovations. Onlythe first argument is compulsory. Ifparam is not supplied, thecurrent parameters inenv are used. Otherwise, they are updatedwith the new parameters and then used. The innovations default to thezero vector.mcss is similar but computes the conditional sum of squares.
Argumentinit can be used to provide initialvalues. If it is missing or NULL, random initial values are generatedfor the free parameters.init may also be a numeric vector suitable for the calloptparam2mcparam(init), see above. This vector would typicallycome from a previous optimisation run.
init may also be a list with elements"eigabs","eigsign","co_r","co_abs". These componentshave the same meaning as the corresponding arguments ofxx.ss.
TODO: more is needed here!
Value
A list with the following components:
fmcss | a function to compute the sum of squares for a model. |
fparamvec | a function to convert mc-parameters to optimisationparameters. |
fmcparam | a function to convert optimisation parameters tomc-parameters. |
env | an object of class |
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
See Also
xx.ss which is called bymC.ss
Examples
# test0 rootsspec.coz2 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(2,4))spec.coz2xxcoz2a <- mC.ss(spec.coz2)## test0 rootsspec.coz4 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(3,4))xxcoz4a <- mC.ss(spec.coz4)Methods for function maxLag() in package 'pcts'
Description
Methods for function maxLag() in package 'pcts'.
Methods
signature(object = "PeriodicArmaFilter")
Examples
## non-periodic autocovariancesmaxLag(autocovariances(AirPassengers))## periodicpcts_exdata() # creates ap, ap7to9, pcfr, pcfr2to4,maxLag(autocovariances(ap, maxlag = 6))## pcarma filterm <- rbind(c(0.81, 0), c(0.4972376, 0.4972376))ar_filt3 <- new("PeriodicBJFilter", coef = m, order = c(1,2))arma_filt3 <- new("PeriodicArmaFilter", ar = ar_filt3)maxLag(arma_filt3)Class mcOptimCore
Description
Class mcOptimCore.
Extends
All reference classes extend and inherit methods from"envRefClass".
Fields
flag.exploring:Object of class
logical~~private.counter.fn:Object of class
integer~~period:Object of class
integer~~len.block:Object of class
integer~~n_col:Object of class
integer~~r_col:Object of class
integer~~cp_col:Object of class
integer~~ind.r.eigval:Object of class
integer~~r_ind:Object of class
integer~~ind.cp.eigval:Object of class
integer~~cp_ind:Object of class
integer~~filter.order:Object of class
integer~~ev_abs:Object of class
matrix~~ev_sign:Object of class
matrix~~co_r:Object of class
matrix~~co_arg:Object of class
matrix~~flag.generators:Object of class
logical~~par.ind:Object of class
ANY~~auto.ind:Object of class
ANY~~inf.ind:Object of class
ANY~~universe:Object of class
ANY~~col.minusinf.ind:Object of class
ANY~~col.inf.ind:Object of class
ANY~~ind1:Object of class
integer~~ind2:Object of class
integer~~ind3:Object of class
integer~~ind4:Object of class
integer~~n1:Object of class
integer~~n2:Object of class
integer~~n3:Object of class
integer~~n4:Object of class
integer~~seqn1:Object of class
integer~~seqn2:Object of class
integer~~seqn3:Object of class
integer~~seqn4:Object of class
integer~~co:Object of class
matrix~~initmodel:Object of class
ANY~~wrkmodel:Object of class
ANY~~model:Object of class
list~~tempnam:Object of class
ANY~~param_names:Object of class
character~~lo_bound:Object of class
ANY~~up_bound:Object of class
ANY~~mcss.cnt:Object of class
integer~~wrkev:Object of class
ANY~~
Methods
mclik(param, x, eps):~~
minimBBlu(x, ..., CONDLIK):~~
mcss(param, x, eps):~~
matepshat(param, x, eps):~~
process.mcss.cnt(mclik, mepshat):~~
sigma2hat(param, x, eps):~~
initialize(...):~~
mcparam2optparam():~~
optparam2mcparam(param):~~
minimBB(x, ..., CONDLIK):~~
optimize(optimfn, mcmethod, x, ..., MCBOUNDS):~~
mcsigma2(param, x, eps):~~
minim(x, ..., CONDLIK):~~
Examples
showClass("mcOptimCore")Asymptotic covariance matrix of periodic mean
Description
Asymptotic covariance matrix of periodic mean.
Usage
meanvarcheck(parmodel, n)meancovmat(parmodel, n, cor = FALSE, result = "var")Arguments
parmodel | a periodic model. |
n | number of observations (TODO: need clarification here). |
cor | if |
result | if |
Details
Computes asymptotic covariance or correlation matrix of the periodicmeans.
Value
ifresult = "var" a matrix,otherwise a vector
Author(s)
Georgi N. Boshnakov
See Also
Examples
x <- arima.sim(list(ar=0.9), n=1000)proba1 <- fitPM(c(3,2,2,2), x)meancovmat(proba1, 100)meancovmat(proba1, 100, cor = TRUE)meancovmat(proba1, 100, result = "")meancovmat(proba1, 100, cor = TRUE, result = "")meanvarcheck(proba1, 100)Get the cycle of a periodic object
Description
Get the cycle of a periodic object, a generic function.
Usage
modelCycle(object)modelCycle(object, ... ) <- valueArguments
object | an object. |
value | the new value for the cycle, an object inheriting from |
... | not used. |
Details
modelCycle is essentially internal, for programming. The userlevel function to get the cycle of an object ispcCycle.
modelCycle returns the Cycle object (in the sense of packagepcts), associated withobject.modelCycle is ageneric function which makes it possible to associate a cycle withobjects from a class, without inheriting from the cycle classes.
By definition,NULL represents the model cycle of objects fromclasses with no (inherited) method formodelCycle.
The default method ofmodelCycle returnsNULL.The default method for its replacement version throws error.
Value
formodelCycle, an object inheriting from class"BasicCycle" orNULL;
"modelCycle<-" is used for the side effect of changing thecycle ofobject.
Methods
signature(object = "ANY")signature(object = "ModelCycleSpec")
Basic information about periodic ts objects
Description
Basic information about periodic periodic time series objects.
Usage
nCycles(x, ...)nTicks(x)nVariables(x, ...)nSeasons(object)Arguments
x,object | an object from a periodic time series class. |
... | further arguments for methods. |
Details
nTicks gives the number of time points, i.e. number of rows inthe matrix representation.
nVariables gives the number of variables in the time series.
nSeasons gives the number of seasons of time series and otherperiodic objects.
nCycles gives the number of cycles available in the data,e.g. number of years for monthly data. It always gives an integernumber. Currently, if the result is not an integer an error israised.TODO: There is a case to round up or give the number of fullcycles available but this seems somewhat dangerous if done quietly. Agood alternative is to provide argument for control of this.
There are further functions to get or set the names of the units ofseason and the seasons, seeallSeasons.
Value
an integer number
Author(s)
Georgi N. Boshnakov
See Also
Examples
ap <- pcts(AirPassengers)nVariables(ap)nTicks(ap)nCycles(ap)nSeasons(ap)monthplot(ap)boxplot(ap)Number of seasons of a periodic object
Description
Number of seasons of a periodic object.
Usage
## S4 method for signature 'Cyclic'nSeasons(object)## same signature for all periodic classes in package "pcts"Arguments
object | an object for which the notion of number of seasons makes sense. |
Details
nSeasons is a generic function. This page gives is for themethods defined in package"pcts" - all periodic classes have(or inherit) a method.
Value
an integer number
Methods
signature(object = "DayWeekCycle")signature(object = "MonthYearCycle")signature(object = "PeriodicIntegratedArmaSpec")signature(object = "QuarterYearCycle")signature(object = "PeriodicMonicFilterSpec")signature(object = "PeriodicInterceptSpec")signature(object = "Cyclic")signature(object = "BareCycle")signature(object = "OpenCloseCycle")signature(object = "Every30MinutesCycle")signature(object = "PartialCycle")signature(object = "VirtualPeriodicModel")signature(object = "SarimaFilter")signature(object = "VirtualArmaFilter")
Author(s)
Georgi N. Boshnakov
See Also
allSeasons for other functions related to theseasonality of an object;
nCycles for related functions
Examples
## scalar time seriesap <- pcts(AirPassengers)nSeasons(ap) # 12## multivariate time seriespcfr <- pcts(dataFranses1996)nSeasons(pcfr) # 4## five-day-week periodfive_day_week <- BuiltinCycle(5)five_day_weeknSeasons(five_day_week)Number of observations in a time series
Description
Number of observations in a time series.
Methods
signature(x = "matrix")signature(x = "numeric")signature(x = "PeriodicTimeSeries")signature(x = "Cyclic")
Fit PAR model using sample autocorrelations
Description
Fit PAR model using sample autocorrelations.
Usage
num2pcpar(x, order, result = NULL, ...)Arguments
x | time series, a numeric vector. |
order | PAR order, a single number or a vector with one entry foreach season. |
result | what to return, the default is to return the full model,see Details. |
... | passed on to |
Details
Computes the periodic autocorrelations and fits a PAR model using thePeriodic Levinson-Durbin algorithm.
The order is a vector of non-negative integers, specifying theautoregressive orders for each season. Iforder is a singlenumber, then all seasons have that order.
mean controls centering in the computation of theautocorrelations. Ifmean is numeric, then subtract thesupplied mean before computing the autocovariances. Ifmean isTRUE, the default, compute and subtract the sample periodic meanbefore computing the autocovariances. Ifmean is FALSE, do notcentre the series, i.e. assume that the mean is zero.
Ifresult is NULL, the default, returns the full model. Ifresult = "coef", returns the PAR coefficients only (currentlyany value ofresult other than NULL has this effect).
Value
The coefficients of the fitted model or a list with components:
mean | the mean, set as described in Details. |
coef | forward prediction coefficients. |
scale | standard deviations of the innovations. |
Author(s)
Georgi N. Boshnakov
See Also
fitPM which usesnum2pcpar for calculations
Examples
## Not run: simts1 <- matrix(rnorm(100), nrow = 4)num2pcpar(simts1, order = c(3,2,2,2), period = 4 )num2pcpar(simts1, order = c(3,2,1,2), period = 4 )pdSafeParOrder(c(3,2,1,2))pdSafeParOrder(c(3,2,2,1))num2pcpar(simts1, order = c(3,2,2,1), period = 4 )num2pcpar(simts1, order = pdSafeParOrder(c(3,2,2,1)), period = 4 )num2pcpar(simts1, order = c(3,2,1,2), period = 4 )num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = rep(0,4) )num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )$coef@m - num2pcpar(simts1, order = c(3,2,1,2), period = 4 )$coef@m## End(Not run)Compute asymptotic covariance matrix for PAR model
Description
Compute asymptotic covariance matrix for PAR model
Usage
parcovmatlist(parmodel, n, cor = FALSE, result = "list")Arguments
parmodel | PAR model, object of class |
n | length of the series or a vector with one element for eachseason. |
cor | If TRUE return correlation matrix. |
result | if "list", the default, return a list, if "Matrix"return a Matrix object, otherwise return an ordinary matrix, seeDetails. |
Details
Uses eq. (3.3) in the reference.
Ifresult = "list",parcovmatlist returns a list whoses-th element is the covariance matrix of the PAR parameters for thes-th season. Otherwise, ifresult = "Matrix" it returns ablock-diagonal matrix created by.bdiag() from package"Matrix". Ifresult = "matrix" it returns an ordinary matrix(with the current implementation this is returned for any value otherthan "list" or "Matriix").
Value
a list, matrix or block-diagonal matrix, as described in Details
Author(s)
Georgi N. Boshnakov
References
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
See Also
Examples
x <- arima.sim(list(ar=0.9), n=1000)proba1 <- fitPM(c(3,2,2,2), x)parcovmatlist(proba1, 100)parcovmatlist(proba1, 100, cor = TRUE)sqrt(diag(parcovmatlist(proba1, 100, cor = TRUE)[[1]]))meanvarcheck(proba1, 100)Compute periodic partial autocorrelations
Description
Methods for computation of periodic partial autocorrelations.
Methods
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "ANY")
See Also
partialAutocorrelations in packagesarimafor further details.
partialVariances,partialAutocovariances
Compute periodic partial autocovariances
Description
Compute periodic partial autocovariances.
Methods
signature(x = "VirtualPeriodicAutocovariances")
See Also
partialAutocorrelations in packagesarimafor further details.
partialAutocorrelations,partialVariances
Compute periodic partial coefficients
Description
Methods for computation of periodic partial coefficients.
Methods
signature(x = "PeriodicArModel")signature(x = "VirtualPeriodicAutocovariances")
Compute periodic partial variances
Description
Compute periodic partial variances.
Methods
signature(x = "VirtualPeriodicAutocovariances")
See Also
partialVariances in packagesarimafor further details.
partialAutocorrelations for for partial autocorrelations.
Applies a periodic ARMA filter to a time series
Description
Filter time series with a periodic arma filter.Ifwhiten isFALSE (default) the function appliesthe given ARMA filter toeps (eps is often periodicwhite noise). Ifwhiten isTRUE the function appliesthe “inverse filter” tox, effectively computingresiduals.
Usage
pc.filter(model, x, eps, seasonof1st = 1, from = NA, whiten = FALSE, nmean = NULL, nintercept = NULL)Arguments
x | the time series to be filtered, a vector. |
eps | residuals, a vector or NULL. |
model | the model parameters, a list with components |
seasonof1st | the season of the first observation (i.e., of x[1]). |
from | the index from which to start filtering. |
whiten | if TRUE use |
nmean | a vector of means having the length of the series, see Details. |
nintercept | a vector of intercepts having the length of the series, see details. |
Details
The model is specified by argumentmodel, which is a list withthe following components:
phithe autoregression parameters,
thetathe moving average parameters,
pthe autoregression orders, a single number or avector with one element for each season,
qthe moving average orders, a single number or avector with one element for each season,
periodnumber of seasons in a cycle,
meanmeans of the seasons,
interceptintercepts of the seasons.
The relation betweenx andeps is assumed to be thefollowing. Let
y_t = x_t - mu_t
be the mean corrected series, wheremu_t is the mean, see below.The equation relating themean corrected series,y_t=x_t - \mu_t, andeps is the following:
y_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t
wherec_t is the intercept,nintercept. The inversefilter is obtained by writing this as an equation expressing\varepsilon_t through the remaining quantities.
Ifwhiten = TRUE,pc.filter uses the above formula tocompute the filtered values ofx fort=from,...,n,i.e. whitening the time series ifeps is white noise. Ifwhiten = FALSE,eps is computed, i.e. the inverse filteris appliedx fromeps, i.e. “colouring”x.In both cases the first few values inx and/oreps areused as initial values.
Essentially, the mean is subtracted from the series to obtain themean-corrected series, sayy. Then eithery is filteredto obtaineps or the inverse filter is applied to obtainy fromepsfinally the mean is added back toy and the result returned.
The mean is formed bymodel$mean and argumentnmean. Ifmodel$mean is supplied it is recycled periodically to thelength of the seriesx and subtracted fromx. Ifargumentnmean is supplied, it is subtracted fromx. Ifbothmodel$mean andnmean are supplied their sum issubtracted fromx.
The above gives a vectory,y_t=x_t - \mu_t, which is then filtered. If the mean iszero,y_t=x_t in the formulas below.
Finally, the mean is added back,x_t=y_t+\mu_t, and the newx is returned.
The above gives a vectory which is used in the filtering. Ifthe mean is zero,y_t=x_t in the formulae below.
pc.filter can be used to simulate pc-arma series with thedefault value ofwhiten=FALSE. In this caseeps is theinput series andy the output.
y_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t
Thenmodel$mean ornmean are added toy to form theoutput vectorx.
Residuals corresponding to a seriesy can be obtained bysettingwhiten=TRUE. In this casey is the input series.The elements of the output vectoreps are calculated by theformula:
\varepsilon_t = - c_t - \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} - \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + y_t
There is no need in this case to restorex sinceeps isreturned.
In both cases any necessary initial values are assumed to be alreadyin the vectors. Iffrom is not supplied it is chosen as thesmallesti such that for allt\ge i,t-p[t]>0 andt-q[t]>0, i.e. the filter will not requirenegative indices forx oreps.
pc.filter calls the lower level functionpc.filter.xarmato do the computation.
Value
The filtered series: the modifiedx ifwhiten=FALSE, themodifiedeps ifwhiten=TRUE.
Level
1
Author(s)
Georgi N. Boshnakov
See Also
the lower level functionspc.filter.xarma which do the computations
Filter time series with periodic arma filters
Description
Filter time series with periodic arma filters with or options forperiodic and non-periodic intercepts.
Usage
pc.filter.xarma(x, eps, phi, theta, period, p, q, n, from, seasonof1st = 1, intercept = NULL, nintercept = NULL)Arguments
x | the time series to be filtered, a vector. |
eps | the innovations, a vector. |
phi | the autoregression parameters, a matrix. |
theta | the moving average parameters, a matrix. |
period | the period (number of seasons in a year). |
p | the autoregression orders, recycled to |
q | the moving average orders, recycled to |
n | a positive integer, the time index of the last observation to befiltered. |
from | a positive integer, the time index of the first observation to befiltered. |
seasonof1st | a positive integer, the season of the time index of |
intercept | the intercepts of the seasons, a vector of length |
nintercept | intercepts, a vector of the same length as |
Details
pc.filter.xarma is somewhat lower level.The user level function ispc.filter which usespc.filter.xarma to do the computations.
pc.filter.xarma filters the time seriesx by thefollowing formula (fort=from,...,n):
x_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)x _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t,
wherec_t is the overall intercept at timet, seebelow. Values ofx[t] fort outside the rangefrom,n, if any, are left unchanged. Values fort<fromare used as initial values when needed.
Two intercepts are provided for convenience and some flexibility. Theperiodic intercept,intercept, is a vector of lengthperiod. It is replicated to lengthn, taking care toensure that the first element of the resulting vector, saya,starts withintercept[seasonof1st].nintercept can bean arbitrary vector of lengthn. It can be used to representtrend or contributions from covariates.nintercept is notnecessarilly periodic and argumentseasonof1st does not affectits use. The overall intercept is obtained as the sumc = a + nintercept.
Usuallyx is a numeric vector but it can also be a matrix inwhich each column represents the data for one “year”.Also, the length ofx is typically, but not necessarilly, equalton. It is prudent to ensure thatlength(x) >= n andthis must be done ifx is a matrix.
Argumentphi is ignored ifp==0,argumenttheta is ignored ifq==0.
pc.filter.xarma is meant to be called by other functions whosetask is to prepare the arguments with proper checks. It does not makemuch sense to repeat the checks inpc.filter.xarma. Inparticular, no check is made to ensure thatfrom andnare correctly specified.
This is a low level function meant to be used with basic vectorsand matrices. TODO: Implement in C/C++. In the currentimplementation. it accesses the elements of the arguments withstraightforward indexing, so objects from classes may be used aswell, provided thatx[t],eps[t],phi[t,i],theta[t,i], as well as assignment tox[t], are definedfor scalar indices.
Value
Returnsx withx[from] tox[n] filled with thefiltered values and values outside the intervalfrom,...,nleft unchanged.
The mode ofx is left unchanged. In particular,x may bea matrix with each row representing the data for a season. This isconvenient since periodic time series are often more easily processedin this form.
Level
0 (base)
Author(s)
Georgi N. Boshnakov
See Also
function to compute estimates of the h weights
Description
The h coefficients are scaled cross-covariances between the timeseries and the innovations. This function computes estimates for husing as input the observed series, a series of estimated innovations,and an estimate of the variance of the innovations.
Usage
pc.hat.h(x, eps, maxlag, si2hat)Arguments
x | the observed time series x(t) |
eps | a series of esimated innovations |
maxlag | maximum lag |
si2hat | estimate of the variance of the innovations |
Details
If missing, the variance of the innovations is estimated fromeps.
Value
A matrix of the coefficient up to lag maxlag with one row for each season.
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
Compute periodic autocorrelations from PAR coefficients
Description
Compute periodic autocorrelations from PARcoefficients. This effectively solves the inverse problem to thatsolved by the periodic Levinson-Durbin algorithm but does not use arecursion.
Usage
pcAR2acf(coef, sigma2, p, maxlag = 10)Arguments
coef | PAR coefficients, a matrix, see Details. |
sigma2 | innovations variances. |
p | PAR order. |
maxlag | How many lags to compute. |
Details
coef is a matrix with the coefficients for seasoni inthe i-th row. The coefficients start from lag 1.
The first few autocorrelations are computed by solving a linearsystem, see the references. The rest, are generated using the periodicYule-Walker equations.
Value
a matrix, in which rows contains the acf's for seasonsfor lags 0, 1, ..., maxlag (in this order).
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
Boshnakov GN, Boteva A (1992).“An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.”Varna.
See Also
pcarma_acvf_lazy, which does the main computation, but notethat the coefficients for it start from lag zero
Examples
m <- rbind( c(0.81, 0), c(0.4972376, 0.4972376) )si2 <- PeriodicVector(c(0.3439000, 0.1049724))pcAR2acf(m)pcAR2acf(m, si2)pcAR2acf(m, si2, 2)pcAR2acf(m, si2, 2, maxlag = 10)# same using pcarma_acvf_lazy directlym1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )testphi <- slMatrix(init = m1)myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 10)myf(1:2, 0:9) # get a matrix of valuesall(myf(1:2, 0:9) == pcAR2acf(m, si2, 2, maxlag = 9)) # TRUEApply a function to each season
Description
Apply a function to each season.
Usage
pcApply(object, ...)## S4 method for signature 'numeric'pcApply(object, nseasons, FUN, ...)## S4 method for signature 'matrix'pcApply(object, nseasons, FUN, ...)## S4 method for signature 'PeriodicTS'pcApply(object, FUN, ...)## S4 method for signature 'PeriodicMTS'pcApply(object, FUN, ...)Arguments
object | an object for which periodic mean makes sense. |
nseasons | number of seasons. |
FUN | a function, as for |
... | further arguments for |
Details
For univariate periodic time series,pcApply appliesFUNto the data for each season. For multivariate periodic time series,this is done for each variable.
The methods for"numeric" and"matrix" are equivalent tothose for"PeriodicTS" and"PeriodicMTS",respectively. The difference is that the latter two don't needargumentnseasons and take the names of the seasons fromobject.
Argument"..." is for further arguments toFUN. Inparticular, with many standardR functions argumentna.rm = TRUE can be used to omit NA's, see the examples.
In the univariate case, whenlength(object) is an integermultiple of the number of seasons the periodic mean is equivalent toapply(matrix(object, nrow = nseasons), 1, FUN, ...).
Value
numeric or matrix for the methods described here, see sectionDetails.
Methods
signature(object = "matrix")signature(object = "numeric")signature(object = "PeriodicMTS")signature(object = "PeriodicTS")
Author(s)
Georgi N. Boshnakov
See Also
Examples
pcApply(pcts(presidents), mean, na.rm = TRUE)pcMean(pcts(presidents), na.rm = TRUE) # samepcApply(pcts(presidents), median, na.rm = TRUE)pcApply(pcts(presidents), var, na.rm = TRUE)pcApply(pcts(presidents), sd, na.rm = TRUE)pcfr2to4 <- pcts(dataFranses1996)[2:4]pcApply(pcfr2to4, median, na.rm = TRUE)pcApply(pcfr2to4, sd, na.rm = TRUE)Compute the sum of squares for a given PAR model
Description
Compute the sum of squares for a given PAR model.
Usage
pcAr.ss(x, model, eps = numeric(length(x)))Arguments
x | time series, a numeric vector. |
model | a model. |
eps | residuals, defaults to a vector of zeroes. This may be usedfor models with moving average terms, for example. |
Details
todo:
Value
a number
Author(s)
Georgi N. Boshnakov
Create or extract Cycle objects
Description
pcCycle() is a generic function with methods for creating,converting, modifying, and extracting cycle objects.BuiltinCycle() is a function to create cycle objects from the builtin cycle classes.
Usage
pcCycle(x, type, ...)BuiltinCycle(n, coerce = FALSE, first = 1, stop = TRUE)Arguments
x | an object, methods include numeric, character and cyclic objects,see Details. |
type | class of the result. If equal to |
... | further arguments for methods. |
n | number of seasons, an integer. |
coerce | if |
first | which season is first for this object. |
stop | if |
Details
pcCycle serves as both a constructor and extractor of cycleobjects. It is meant to just do the right thing, relieving the userfrom the burden of specifying a particular cycle class.
Ifx is numeric it constructs a cycle object with periodx and additional properties as specified by the otherarguments. Ifx is a character string, it is taken to be thename of one of the builtin cycles.
pcCycle can be used to create a modified version of a cycleobject and/or convert it to another cycle type. This is done byproviding a cycle object as argumentx, i.e. one inheritingfrom"BasicCycle".
Ifx inherits from"Cyclic",pcCycle returns itscycle component.
Argumenttype should be rarely needed, except maybe toconveniently force conversion of the builtin type to an ordinary type.
The descriptions of the individual methods in section Methods givesome further specific details.
BuiltinCycle is a convenience function to create objects frombuiltin cycle classes by specifying the number of seasons. Thebuiltin cycle classes are esseintially fixed, except that which seasonis considered first can be changed using argumentfirst. Ifother modifications are desired, convert the returned builtin cycleobject to class"SimpleCycle". This can be done also in thecall toBuiltinCycle() by specifyingcoerce = TRUE.
By default,BuiltinCycle throws an error if there is no builtinclass with the requested number of seasons. Set argumentstopto FALSE to create an object from class"BareCycle" instead(and it will be converted to"SimpleCycle" ifcoerce = TRUE). Argumentstop is mainly for programming.
Value
forpcCycle, an object from one of the cycle classes;
forBuiltinCycle, an object from one of the builtin classes,coerced if requested.
Methods
signature(x = "numeric", type = "missing")creates a cycle object with period
x. Ifxis the onlyargument, a"BareCycle"object is created, otherwise theconstructor of"SimpleCycle"is invoked with all argumentsexcepttypepassed on to it.signature(x = "character", type = "missing")creates an object from the class specified by
x.Currently this is equivalent tonew(x, ...)but somewhatmore portable. Future amendments may use a more suitable classfor some combinations of the arguments. Also, if a class is renamed,a code will be inserted here to create an equivalent object.signature(x = "numeric", type = "character")signature(x = "character", type = "character")first call the method with
type = "missing", thenconvert the result to classtype.signature(x = "Cyclic", type = "ANY")extracts the cycle component of
x(x@cycle).Currently ignores the remaining arguments.signature(x = "BasicCycle", type = "missing")convert an object from any cycle class to class
"SimpleCycle". This is likeas(x, "SimpleCycle")butcan have further arguments.signature(x = "BasicCycle", type = "character")convert an object from any cycle class to class
type.signature(x = "ts", type = "missing")signature(x = "ts", type = "character")when
xis of class"ts", extract the frequency andconvert it to a cycle class. Just as for"ts", certainfrequencies are taken to correspond to specific classes. While baseR treats periodicities 4 and 12 specially,pcCycleextendsthis to all builtin classes in pcts. Argumenttypecan beused to overwrite this default behaviour by requesting a specificclass. In particular,type = "BareCycle"andtype = ""cause the result to be"BareCycle".signature(x = "PeriodicTimeSeries", type = "missing")signature(x = "PeriodicTimeSeries", type = "character")extract the cycle part of an object inheriting from
"PeriodicTimeSeries", currently"PeriodicTS"or"PeriodicMTS". Argumenttypecan be used to force theresult to be from a specific cycle class, as in the methods for"ts".
Author(s)
Georgi N. Boshnakov
See Also
allSeasons for further examples,
classBuiltinCycle for the available builtinclasses and more examples,
Pctime for representation of dates and conversionfrom/to datetime objects
Examples
## pcCyclepcCycle(4)pcCycle(4, seasons = c("Spring", "Summer", "Autumn", "Winter"))pcCycle("QuarterYearCycle")BuiltinCycle(4) # same, recommendedpcCycle("QuarterYearCycle", type = "BareCycle")pcCycle("QuarterYearCycle", type = "SimpleCycle")## BuiltinCycleBuiltinCycle(2) # "OpenCloseCycle"BuiltinCycle(4) # "QuarterYearCycle"BuiltinCycle(5) # five day week cycleBuiltinCycle(7) # "DayWeekCycle"BuiltinCycle(12) # "MonthYearCycle"BuiltinCycle(48) # "Every30MinutesCycle"## error, since there is no builtin cycle with 19 seasons:## BuiltinCycle(19)## use stop = FALSE to reate a default cycle in this caseBuiltinCycle(19, stop = FALSE)BuiltinCycle(19, coerce = TRUE, stop = FALSE)Compute periodic mean
Description
Compute periodic mean, generic function.
Usage
pcMean(object, ...)## S4 method for signature 'numeric'pcMean(object, nseasons, ...)## S4 method for signature 'matrix'pcMean(object, nseasons, ...)## S4 method for signature 'PeriodicTS'pcMean(object, ...)## S4 method for signature 'PeriodicMTS'pcMean(object, ...)Arguments
object | an object for which periodic mean makes sense. |
nseasons | number of seasons. |
... | further arguments for methods. |
Details
For univariate periodic time series,pcMean computes the meanfor each season and returns a named vector. For multivariate periodictime series, the result is a matrix with one column for each variable.
The methods for"numeric" and"matrix" are equivalent tothose for"PeriodicTS" and"PeriodicMTS",respectively. The difference is that the latter two don't needargumentnseasons and take the names of the seasons fromobject.
Argumentna.rm = TRUE can be used to omit NA's.
In the univariate case, whenlength(object) is an integermultiple of the number of seasons the periodic mean is equivalent tocomputing the row means ofmatrix(object, nrow = nseasons).
Value
numeric or matrix for the methods described here, see section‘Details’.
Methods
signature(object = "matrix")signature(object = "numeric")signature(object = "PeriodicMTS")signature(object = "PeriodicTS")signature(object = "VirtualPeriodicArmaModel")
Author(s)
Georgi N. Boshnakov
See Also
pcApply which applies an arbitrary function by season
Examples
pcMean(pcts(presidents))pcMean(pcts(presidents), na.rm = TRUE)pcMean(pcts(dataFranses1996)[2:5], na.rm = TRUE)pcMean(1:20, nseasons = 4)m <- matrix(1:20, nrow = 4)all(apply(m, 1, mean) == pcMean(1:20, nseasons = 4)) # TRUEPlot periodic time series
Description
Plot periodic time series.
Usage
## S3 method for class 'PeriodicTimeSeries'boxplot(x, ...)## S3 method for class 'PeriodicTimeSeries'monthplot(x, ylab = deparse(substitute(x)), base, ...)Arguments
x | a periodic time series object. |
... | further arguments to be passed to the plotting function. |
ylab | label for the y-axis, only used for univariate time series. |
base | a function for use for computing reference lines. |
Details
Functions for periodic/seasonal plots and boxplots.
Author(s)
Georgi N. Boshnakov
See Also
Examples
ap <- pcts(AirPassengers)monthplot(ap)boxplot(ap)fr23 <- pcts(dataFranses1996[ , 2:3])monthplot(fr23)boxplot(fr23)Test for periodicity
Description
Test for periodicity
Usage
pcTest(x, nullmodel, nseasons, ...)Arguments
x | the object to be tested, e.g. a time series or a periodic acf |
nullmodel | specification of the test to be performed |
nseasons | number of seasons |
... | additional arguments to be passed on to methods |
Details
This is a generic function which acts as a dispatcher for varioustests for periodicity and periodic correlation.
x is typically a time series but conceptually it is an objectcontaining the statistics needed for carrying out the requested test.For example,x may be the periodic autocovariance function fortests based on sample autocorrelations and autocovariances.
The method with signature(x = "ANY", nullmodel = "character") maybe considered as default forpcTest. The “real” defaultmethod simply prints an error message.
Value
a list containing the results of the requested test,see the individual methods for details
Methods
signature(x = "ANY", nullmodel = "character")Argument
nullmodelspecifies the test to be performed.It should be a single character string. If it is one ofthe strings recognised by this method, the test specified below iscarried out. Otherwisenullmodelis taken to be the name of afunction which is called with arguments(x,...).Currently, the following character strings are recognised:
- "wn"
Box test for (non-periodic) white noise, simply calls
Box.test.- "piar"
Franses (1996) test for periodic integration.
signature(x = "slMatrix", nullmodel = "character")xhere is the periodic autocovariance function. This methodworks similarly to the method for signature(x = "ANY", nullmodel = "character"), see its description.Currently, the following character strings are recognised:
- "pwn"
Ljung-Box test for periodic white noise,
- "periodicity"
McLeod test for periodic correlation.
signature(x = "numeric", nullmodel = "character")signature(x = "PeriodicTimeSeries", nullmodel = "character")
Note
TODO: critical values
Author(s)
Georgi N. Boshnakov
See Also
test_piar,pwn_McLeodLjungBox_testperiodic_acf1_test
Examples
cu <- pcts(dataFranses1996[ , "CanadaUnemployment"])cu <- window(cu, start = availStart(cu), end = availEnd(cu))test_piar(cu, 4, 1, sintercept = TRUE)pcTest(cu, "piar", 4, 1, sintercept = TRUE)Compute normalising factors
Description
Compute a matrix of factors such that elementwise division of theperiodic autocovariance matrix by it will give the periodicautocorrelations.
Usage
pc_sdfactor(sd, maxlag)Arguments
sd | standard deviations of the seasons numeric. |
maxlag | maximal lag, a number. |
Value
a matrix of coefficients of sizeperiod x (maxlag+1). Thelength ofsd is taken to be the period.
Author(s)
Georgi N. Boshnakov
See Also
Examples
## equivalent to data(Fraser, package = "pear")Fraser <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12))logfraser <- window(pcts(log(Fraser)), start = c(1913, 1))acvf1 <- autocovariances(logfraser, maxlag = 2)fac <- pc_sdfactor(sqrt(acvf1[ , 0]), 2)fac[ , 1:3]acrf1 <- autocorrelations(logfraser, maxlag = 2)all.equal(acvf1[], acrf1[] * fac) # TRUECompute PAR autocovariance matrix
Description
Compute PAR autocovariance matrix
Usage
pc.acf.parModel(parmodel, maxlag = NULL)pcacfMat(parmodel)Arguments
parmodel | PAR model, an object of class |
maxlag | maximum lag |
Details
pc.acf.parModel returns the autocovariances of a PAR model inseason-lag form with maximum lag equal tomaxlag. Ifmaxlag is larger than the available precomputedautocovariances, they missing ones are computed using the Yule-Walkerrelations. Note thatpc.acf.parModelassumes that there are enough precomputed autocovariances to use theYule-Walker recursions directly.
TODO:pc.acf.parModel is tied to the old classes since it accessestheir slots. Could be used as a template to streamline the method forautocovariances for class"PeriodicAutocovariance".
The season-lag form can be easily converted to other forms with thepowerful indexing operator, see the examples andslMatrix-class.
pcacfMat is a convenience function for statisticalinference. It creates a covariance matrix with dimension chosenautomatically. This covariance matrix is such that the asymptoticcovariance matrix of the estimated parameters can be obtained by dividingsub-blocks by innovation variances and inverting them. See,eq. (3.3) in the reference.
Value
forpcacfMat, a matrix
forpc.acf.parModel, anslMatrix
Author(s)
Georgi N. Boshnakov
References
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
See Also
Examples
x <- arima.sim(list(ar = 0.9), n = 1000)proba1 <- fitPM(c(3,2,2,2), x)acfb <- pc.acf.parModel(proba1, maxlag = 8)acfb[4:(-2), 4:(-2), type = "tt"]pcacfMat(proba1)Variances of sample periodic autocorrelations
Description
Computes the variances of sample periodic autocorrelations fromperiodic white noise.
Usage
pcacf_pwn_var(nepoch, period, lag, season)Arguments
lag | desired lags, a vector of positive integers. |
season | desired seasons. |
nepoch | number of epochs. |
period | number of seasons. |
Details
These are given by McLeod (1994), see the reference, eq. (4.3).
Value
A matrix whose (i,j)th entry contains the variance of theautocorrelation coefficient for seasonseason[i] and laglag[j].
Author(s)
Georgi N. Boshnakov
References
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
Examples
pcacf_pwn_var(79, 12, 0:16, 1:12)Periodic Levinson-Durbin algorithm
Description
Calculate partial periodic autocorrelations, forward and backwardprediction coefficients and error variances using the periodicLevinson-Durbin algorithm.
Usage
alg1(r, p)Arguments
r | periodic autocovariances, a matrix, see ‘Details’. |
p | autoregressive orders, numeric vector. |
Details
alg1(r,p) calculates the partial periodic correlations fromautocovariancesr and autoregression ordersp. Thematrixr has the same format as that of ther slot ofpcAcvf objects. The periodicity,d, is set equal tothe number of rows inr. If the length ofp is notequal to the periodicity, all autoregressive orders are set to thefirst element ofp. This last feature is really meant to beused only with a scalarp.
The convention for the signs of the coefficients is the one fromBoshnakov(1996) and is consistent with otherR time seriesfunctions.
pmax below stands for the maximal element ofp,i.e. the maximal AR order.
As in the non-periodic case, the periodic Levinson-Durbin algorithmfits recursively models of order 0, 1, ...,pmax. Namely, atstepi the AR orders for all seasons are set toi. This is done in a way that correctly handles the case whennot all elements ofp are equal, see the references.
The essential quantities calculated by the periodic Levinson-Durbinalgorithm are returned as matrices, whoseith rowscontain values for seasoni. The complete details depend onthe quantities, as described below.
The partial autocorrelations, the forward innovation variances andthe backward innovation variances are returned as matrices withd rows and1+pmax columns, whose j-th columns containthe quantities for order j-1 (partial autocorrelations, forwardinnovation variances and backward innovation variances, respectively).Note that the lag-0 partial autocorrelations are the autocovariancesfor lag 0, see the references for details.
The forward autoregression parameters are returned as a list whosejth element is a matrix containing the coefficients fororderj. Similarly for the backward autoregression parameters.
One often is interested in the model of orderp only. Itscoefficients are given byaf[[pmax]], while the innovationvariances are in the last column offv.
Value
A list with the following elements.
orders | autoregression orders |
be | partial autocorrelations, a matrix with d rows |
fv | forward innovation variances, a matrix with d rows |
bv | backward innovation variances, a matrix with d rows |
af | forward autoregression parameters, a list with oneelement for the parameters for each order. |
ab | backward autoregression parameters, a list with oneelement for the parameters for each order. |
Note
The autoregression orders of the output are not necessarilly the sameas those specified in the call. There may be no PAR model with therequested orders, see the references.
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
Lambert-Lacroix S (2000).“On periodic autoregressive process estimation.”IEEE Transactions on Signal Processing,48(6), 1800-1803.
Lambert-Lacroix S (2005).“Extension of autocovariance coefficients sequence for periodically correlated processes.”Journal of Time Series Analysis,26(3), 423-435.
See Also
Examples
r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900))alg1(r1,2)## pc2 <- pcAcvf(init=r1)## pc2a <- pcAcvf(init=r1,seasonnames=c("am","pm"), periodunit="day")# example of Lambert-Lacroixdata(ex1f)pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")res0p2 <- alg1(pc3[],c(0,2))res1p2 <- alg1(pc3[],c(1,2))res3p3 <- alg1(pc3[],c(3,3))paramsys1 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)t1 <- solve(paramsys1$A,paramsys1$b)# this is from tests.r but I have lost t1# set it to pc3 below# note: t1 is not the t1 computed above and in other examples!t1 <- pc3t1t1[]alg1(t1[],c(1,1))alg1(t1[],c(1,0))alg1(t1[],c(0,1))alg1(t1[],c(5,5))alg1(t1[],c(2,2))alg1(t1[],c(2,3))alg1(t1[],c(3,3))alg1(t1[],c(4,4))alg1(t1[],c(5,5))Give partial periodic autocorrelations or other partial predictionquantities for a pcAcvf object.
Description
Give partial periodic autocorrelations or other partial predictionquantities for a pcAcvf object.
Usage
alg1util(x, s, at0 = 1)Arguments
x | an object of a class inheriting from |
s | the required quantity, the name of one of the elements ofthe list returned by |
at0 | if not identical to "var", replace the elements of theresult at lag zero with 1, see ‘Details’. |
Details
This function is a wrapper foralg1(). It callsalg1, todo the computations and returns the requested element as an objectfrom classslMatrix. The model order is set to the maximal lagavialable inx,
Ifat0 is the character string "var", then the lag zero valuesin the result are set to the lag zero autocovariances, otherwise theyare set to 1.This is mainly relevant for the periodic partial autocorrelations(s="be"), since the settingat0="var" ensures that theyare in one to one correspondence with the autocovariances.
Value
the requested quantity as an object of type slMatrix
Author(s)
Georgi N. Boshnakov
References
Lambert-Lacroix S (2000).“On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing,48( 6 ), pp. 1800-1803.
Lambert-Lacroix S (2005).“ Extension of autocovariance coefficients sequence for periodically correlatedprocesses.”Journal of Time Series Analysis,26(6), pp. 423-435.
See Also
Examples
r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900))# example of Lambert-Lacroixdata(ex1f)pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")res0p2 <- alg1(pc3[],c(0,2))res1p2 <- alg1(pc3[],c(1,2))res3p3 <- alg1(pc3[],c(3,3))Fit a PC-ARMA model to a periodic autocovariance function
Description
Fit a PC-ARMA model to a periodic autocovariance function.
Usage
pcarma_acvf2model(acf, model, maxlag)Arguments
acf | a periodic autocovariance function, an object of class |
model | a pc- arma model, an object of class |
maxlag | not used. (todo: check!) |
Value
~Describe the value returnedIf it is a LIST, use
comp1 | Description of 'comp1' |
comp2 | Description of 'comp2' |
...
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
Examples
data(ex1f)pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")# pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)parsys <- pcarma_param_system(pc3, NULL, NULL, c(2,2), 0, 2)param <- solve(parsys$A,parsys$b)# res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0,period=2))# res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0))# res <- pcarma_acvf2model(pc3, list(p=c(1,2),period=2))res <- pcarma_acvf2model(pc3, list(p=c(1,2)))print(param)print(res)Functions to compute various characteristics of a PCARMA model
Description
Given a PCARMA model, create a function for computing autocovariancesor coefficients of the corresponding infinite moving averagerepresentation or prepare the linear system whose solution providesthe first few autocovariances of the model.
Usage
pcarma_acvf_lazy(phi, theta, sigma2, p, q, period, maxlag = 100)pcarma_h_lazy(phi, theta, p, q, period, maxlag = 200)pcarma_acvf_system(phi, theta, sigma2, p, q, period)pcarma_param_system(acf, h, sigma2, p, q, period)pcarma_h(h, na = NA)Arguments
phi | the autoregression parameters, an object of class |
theta | the moving average parameters, an object of class |
sigma2 | the innovation variances, an object of class |
p | the (maximal) autoregression order or the autoregression orders. |
q | the (maximal) moving average order or the moving average orders. |
period | number of seasons in an epoch |
maxlag | maximal lag for which the result is stored internally. |
acf | the autocovariance function, an object of class pcAcvf,slMatrix, or similar |
h |
|
na | not used currently, controls what to do for large lags. |
Details
Compute acvf from parameters
pcarma_acvf_lazy creates a function that will compute (ondemand) values of the acf by a recursive formula. Computed valuesare stored internally for lags up tomaxlag.
System for acvf from parameters
pcarma_acvf_system forms a linear system for the calculationof autocovariances from the parameters of a pc-arma model. Theargumenttheta is not used ifq=0 andphi is notused ifp=0.
System for parameters from acvf
pcarma_param_system takesthe periodic autocovariances of a pc-arma model and computes amatrix and a vector representing the linear system whose solutionprovides the parameters of the model.
Scalarp specifies the same autoregression order for eachseason, similarly forq.p andq may bevectors of lengthperiod specifying the order for each seasonindividually. In the latter case the solution of the system may notbe a proper model or, if it is, its autocovariances may not be theones used here! See the references for details.
The class ofacf is not required to be one of thoseexplicitly listed above, but it should understand their indexingconventions, similarly forsigma2.
For pure autoregression,q=0, the argumentsh andsigma2 are ignored.TODO: add sigma2 (if supplied) tothe returned list?
Compute h from parameters
pcarma_h_lazy: h(t,i) are the coefficients in infinite themoving average representation of the pc.arma model. The calculationsuse formula (4.4) from my paper (or elsewhere) with internal storage(in an slMatrix) of calculated results (for i<maxlag) and recursivecalls to itself. So, it is not necessary to compute h(t,i) in anyparticular order.
Infinite MA coefficients(h)
pcarma_h Function to create a function for lazy computationof h(t,i) in pc.arma models
Takes a matrix of h(t,i) coefficeints and returns a function thatcalculates h(t,i) from my paper xxx. The returned value can be usedin the same way as that ofpcarma_h_lazy.
Value
for pcarma_acvf_lazy
a function taking two argumentst andk such that forscalart andk the callf(t,k) will returnEX(t)X(t-k). If either of the arguments is a vector, thenf(t,k) returns a matrix of size (length(t),length(k))containing the respective autocovariances.
for pcarma_h_lazy
a function, sayh. In calls toh, if both argumentsare scalarsh(t,i) returnsh_{t,i}. If at least one of thearguments is a vector a matrix of values ofh is returned.
for pcarma_acvf_system
a list with two components representing the linear system:
- A
The
(p+1)\mbox{period}\times(p+1)\mbox{period}matrix of the system, an object of class "matrix".- b
The right-hand side of the system, a vector of length
(p+1)\mbox{period}, an object of class "vector".
A^{-1}b can be used to get a vector of theautocovariances in the following order (d is the period, p is themaximal AR order):
K(1,0),...,K(d,0), K(1,1),...,K(d,1),...,K(1,p),...,K(d,p).
for pcarma_param_system
A list with components representing the linear system and the AR andMA orders:
- A
The matrix of the system
- b
The right-hand side of the system
- p
The AR order
- q
The MA order
A^{-1}b will return a vector of the parameters of thepc-arma model: all parameters for the first season, followed by allparameters for the second seasons and so on. For each season theparameters are in the following order (s is the current season, d isthe period,p[s] andq[s] are the corresponding AR andMA orders):
\sigma^2(s), \phi(s,1),...,\phi(s,p[s]),\theta(s,1),...,\theta(s,q[s]).
for pcarma_h
a function, sayh. In calls toh, if both argumentsare scalarsh(t,i) returnsh_{t,i}. If at least one of thearguments is a vector a matrix of values ofh is returned.Analogous topcarma_h_lazy.
Note
forpcarma_acvf_lazy: The recursion may become extremely slow for lags greater thanmaxlag. If large lags are likely to be needed the argumentmaxlag should be used to increase the internal storage. Thedefault formaxlag currently is 100.
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (1996).“Recursive computation of the parameters of periodic autoregressive moving-average processes.”J. Time Ser. Anal.,17(4), 333–349.ISSN 0143-9782,doi:10.1111/j.1467-9892.1996.tb00281.x.
See Also
Examples
## periodic acf of Lambert-Lacroixdata(ex1f)(pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt"))## find the parameterss3 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)coef3 <- solve(s3$A, s3$b)pcarma_unvec(list(p = 2, q = 0, period = 2, param = coef3))## actually, the model is PAR(1,2):s3a <- pcarma_param_system(pc3, NULL, NULL, c(1, 2), 0, 2)coef3a <- solve(s3a$A, s3a$b)pcarma_unvec(list(p = c(1,2), q = 0, period = 2, param = coef3a))## prepare test parameters for a PAR(2) model with period=2.## (rounded to 6 digits from the above example.m1 <- rbind(c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )m2 <- rbind(c(1, 0, 0), c(1, 0, 0) )testphi <- slMatrix(init = m1)testtheta <- slMatrix(init = m2)si2 <- PeriodicVector(c(0.3439000, 0.1049724)) # # or si2 <- c(1,1)## acf from parametersmyf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 110)myf(1,4) # compute a valuea1 <- myf(1:2,0:9) # get a matrix of values## h from parametersh <- pcarma_h_lazy(testphi, testtheta, 2, 2, 2)h(3, 2) # a scalarh1 <- h(1:2, 1:4) # a matrix## compute acvf from parameters( acfsys <- pcarma_acvf_system(testphi, testtheta, si2, 2, 0, 2) )acfvec <- solve(acfsys$A, acfsys$b)acf1 <- slMatrix(acfvec, period = 2)## TODO: examples wirh q != 0Functions for work with a simple list specification of pcarma models
Description
Handle a simple list specification of pcarma models.Functions to convert to and from a representation appropriate forhanding on to optimisation functions.
Usage
pcarma_prepare(model, type)pcarma_unvec(model)pcarma_tovec(model)Arguments
model | specification of a pcarma model, a list, see Details. |
type | not used. |
Details
These functions work with a specification of a pcarma model as a listwith componentsperiod,p,q,param,phi,theta andsi2, see also section ‘Values’.The functions do not necessarily need or examine all these components.
Argumentmodel is a list with components as accepted bypcarma_prepare. Details are below but the guiding rule is thatthere are sensible defaults for absent components.
pcarma_prepare gives a standard representation ofmodel, inthe sense that it ensures that the model has componentsperiod,p andq, such thatp andq are vectors oflengthperiod.pcarma_prepare does not examine any othercomponents of the model. (TODO: do the same for theinnovation variance?)
Ifmodel$period is NULL,pcarma_prepare sets it to thelength of the longer ofmodel$p andmodel$q. Ifmodel$p is a scalar it is extended withrep(model$p, period). Missing or NULLmodel$p is equivalent tomodel$p = 0.model$q is processed analogously.
The net effect is thatperiod,p andq will be setas expected as long asperiod is given or at least one of theother two is of length equal to the period. A warning is issued ifperiod <= 1 (it is all too easy to give scalar values forp andq and forget to set the period, in which caseperiod will be deduced to be one).
A number of functions (includingpcarma_tovec andpcarma_unvec) dealing with the list representation of pcarmamodels start by callingpcarma_prepare to avoid the need forhandling all possible cases.
pcarma_tovec returns a list with componentsp,q andparam, whereparam is a numeric vectorcontaining the pcarma parameters and the innovations variances andthus is suitable for optimisation functions. Notice that it iscomponent param that is a vector. The reason thatpcarma_tovecreturns a list, is that the caller may need to do further work beforecalling a generic optimisation function. For exampe, it may wish todop the variances from the vector.
pcarma_unvec(model) performs the inverse operation. It takes alist like that produced bypcarma_tovec and converts it to adetailed list containing the components of the model.
Value
forpcarma_unvec, a list with components:
p | autoregressive orders, numeric vector |
q | moving average orders, numeric vector |
si2 | innovation variances |
phi | autoregressive parameters |
theta | moving average parameters |
forpcarma_tovec, a list with components:
p | autoregressive order |
q | moving average order |
param | parameters of the model, a numeric vector.TODO: give the order of the parameters in the vector! |
forpcarma_prepare, a list aspcarma_unvec, see alsoDetails.
Note
The specification and the functions were created ad hoc to get thecomputations going and are not always consistent with other parts ofthe package.
Author(s)
Georgi N. Boshnakov
Fit PAR models using least squares
Description
Fit PAR models using least squares. The model may containintercepts and linear trends, seasonal or non-seasonal.
Usage
pclsdf(x, d, lags = integer(0), sintercept = TRUE, sslope = FALSE, intercept = FALSE, slope = FALSE, xreg, contrasts = NULL, seasonof1st = NULL, coefonly = FALSE)Arguments
x | time series, a numeric vector. |
d | period, an integer. |
lags | an integer vector, typically |
sintercept | if TRUE include seasonal intercepts. |
sslope | if TRUE include seasonal linear trend. |
intercept | if TRUE include non-seasonal intercept. |
slope | if TRUE include non-seasonal linear trend. |
xreg | additional regressors, not used currently. |
contrasts | contrasts to use for the seasons factor variable. |
seasonof1st | season of the first observation in the time series,see Details. |
coefonly | if TRUE, return only the parameters of the fittedmodel, otherwise include also the object returned by |
Details
This function fits PAR models by the method of least squares.Seasonal intercepts are included by default. Non-seasonal interceptsare available, as well as seasonal and non-seasonal linear trend.Separate arguments are provided, so that any combination of seasonaland non-seasonal intercepts and slopes can be specified.
Ifcoefonly is TRUE,pclsdf returns only the estimatedparameters, otherwise it includes additional statistical information,see section Note for the current details.
Value
A list with the components listed below. Some components are presentonly if included in the model specification.
par | the PAR coefficients, a matrix with a row for each season. |
sintercept | (if specified) seasonal intercepts, a numeric vector. |
sigma2hat | innovation variances. |
formula.char | the formula used in the call of |
fit | (if |
Note
Currently,pclsdf prepares a model formula according to thespecification and callslm to do the fitting. Component "fit"in the result (available whencoefonly = FALSE) contains theraw fitted object returned bylm. Statistical inference basedon this object would, in general, not be justified for correlateddata.
todo: currently some of the parameters are returned only via thefitted object fromlm.
Author(s)
Georgi N. Boshnakov
See Also
Examples
## data(dataFranses1996)cu <- pcts(dataFranses1996[ , "CanadaUnemployment"])cu <- window(cu, start = availStart(cu), end = availEnd(cu))pclsdf(cu, 4, 1:2, sintercept = TRUE)pclsdf(austres, 4, lags = 1:3)pclsdf(austres, 4, lags = 1:3, sintercept = TRUE)pclsdf(austres, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)x <- rep(1:4,10)pclsdf(x, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)## this is for the version when contrasts arg. was passed on directly to lm.## tmp1 <- pclsdf(austres, 4, lags = 1, sintercept = FALSE, sslope = TRUE,## contrasts = list(Season = "contr.sum" ))Fit a periodically integrated autoregressive model
Description
Fit a periodically integrated autoregressive model.
Usage
pclspiar(x, d, p, icoef = NULL, parcoef = NULL, sintercept = FALSE, seasonof1st = 1, weights = TRUE, itol = 1e-07, maxniter = 1000)Arguments
x | time series. |
d | period. |
p | order of the model, a positive integer, see Details. |
icoef | initial values for the periodic integration coefficients. If missingor |
parcoef | not used currently. |
sintercept | if |
seasonof1st | season of the first observation. |
weights | if |
itol | threshold value for the stopping criterion. |
maxniter | maximum number of iterations. |
Details
This function fits a periodically integrated autoregressive modelusing non-linear least squares. The order of integration is one andthe order of the periodically correlated part isp - 1. So,p must be greater than or equal to one.
Ifweights = TRUE the non-linear optimisation is done withweights inversely proportional to the innovation variances for theseasons, otherwise the unweighted sum of squared residuals isminimised.
Value
a list currently containing the following elements:
icoef | coefficients of the periodic integration filter. |
parcoef | coefficients of the PAR filter. |
sintercept | seasonal intercepts. |
sigma2hat | innovation variances. |
Author(s)
Georgi N. Boshnakov
References
Franses PH (1996).Periodicity and Stochastic Trends In Economic Time Series.Oxford University Press Inc., New York.
Franses PH, Paap R (2004).Periodic Time Series Models.Oxford University Press Inc., New York.
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
See Also
Examples
## see also the examples for fitPM()ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4))pclspiar(ts1, 4, p = 1, sintercept = TRUE)pclspiar(ts1, 4, p = 2, sintercept = TRUE)Create objects from periodic time series classes
Description
Create objects from periodic time series classes.
Usage
pcts(x, nseasons, start, ..., keep = FALSE)Arguments
x | a time series. |
nseasons | number of seasons. This argument is ignored by some methods. |
start | the starting time of the time series, can be a |
keep | if |
... | further arguments to be passed on to methods. |
Details
pcts creates periodic time series objects inheriting from"PeriodicTimeSeries". The particular class depends on argumentsx and, in some cases,keep. The idea is that in normaluse the user does not care about the particular class. See section‘Methods’ for further details.
Familiar functions from base-R work with the objects created bypcts. The help pagewindow describes such methodsand gives examples.
There are also methods foras for conversion to and from thetime series classes defined in packagepcts.
Value
an object inheriting from"PeriodicTimeSeries", the defaultsare"PeriodicTS" for univariate and"PeriodicMTS" andfor multivariate time series.
Methods
signature(x = "numeric", nseasons = "missing")signature(x = "numeric", nseasons = "numeric")signature(x = "numeric", nseasons = "BasicCycle")Creates an object of class
"PeriodicTS", the native class forunivariate periodic time series in package"pcts".signature(x = "matrix", nseasons = "missing")signature(x = "matrix", nseasons = "numeric")signature(x = "matrix", nseasons = "BasicCycle")Creates an object of class
"PeriodicMTS", the native classfor multivariate periodic time series in package"pcts".signature(x = "data.frame", nseasons = "ANY")Currently this just converts
xto matrix and callspctsrecursively. See the methods withx = "matrix"inthe signature.signature(x = "ts", nseasons = "missing")signature(x = "ts", nseasons = "numeric")If
keep = TRUEcreates an object of class"PeriodicTS_ts", otherwise the result is from"PeriodicTS". The number of seasons is taken from the"mts"object.signature(x = "mts", nseasons = "missing")signature(x = "mts", nseasons = "numeric")If
keep = TRUEcreates an object of class"PeriodicMTS_ts", otherwise the result is from"PeriodicMTS". The number of seasons is taken from the"ts"object.signature(x = "xtsORzoo", nseasons = "missing")xneeds to be a regular time series, possibly with missingvalues for some times (technically,zoo::is.regular(x)shouldgive TRUE). For daily time series, the cycle is taken to be day ofweek or a subcycle of it, most commonly Monday-Friday.The implementation of this method is incomplete but for daily datashould work as described.
Author(s)
Georgi N. Boshnakov
See Also
PeriodicTS,PeriodicMTS, the two main periodic time seriesclasses in the package;
dataFranses1996,Fraser2017,four_stocks_since2016_01_01 for further examples;
window for extraction of subsets;
pcApply for applying a function to each season;
Vec,tsVec,pcMatrix for extraction of the core data
Examples
## convert a ts object, no need for further infopcts(AirPassengers, 12)## numericv24 <- rnorm(24)pcts(v24, nseasons = 4) # generic seasonspcts(v24, nseasons = BuiltinCycle(4)) # Quarter/Yearts1 <- pcts(v24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates## select subset of the seasonswindow(ts1, seasons = 3:4)## matrix, multivariate pctsm24 <- matrix(v24, ncol =3)colnames(m24) <- c("A", "B", "C")pcts(m24, nseasons = 4) # generic seasonspcts(m24, nseasons = BuiltinCycle(4)) # Quarter/Yearmts1 <- pcts(m24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with datesmts1## select subset of the seasons for mutivariatewindow(mts1, seasons = 3:4)Deprecated Functions and classes in Packagepcts
Description
These functions and classes are marked for removal and are providedtemporarily for compatibility with older versions of packagepcts only. Use the recommended renamed or new functions instead.
Class"FiveDayWeekCycle" is deprecated, useBuiltinCycle(5) to create objects with equivalentfunctionality, seeBuiltinCycle.
Details
- mCpar
has been renamed to
sim_parCoef- sim_arAcf
has been renamed to
sim_parAcvf
Periodic time series objects for examples
Description
Periodic time series objects for examples and tests. These objects arefrom classes defined in package “pcts” and as a consequence arenot suitable for access withdata().
Usage
pcts_exdata(x, envir = parent.frame())Arguments
x | a character vector giving the names of objects. If missing, allavailable objects will be created. Can also be |
envir | environment where the objects are put, the default is theenvironment of the caller. |
Details
The requested objects are created and put inenvir. Itsdefault is the environment of the caller, which should be sufficientin most use cases.
The following objects are currently available:ap,ap7to9,pcfr,pcfr2to4.
Value
ifx isNA, the names of the available objects.Otherwise the function is called for the side effect of creatingobjects inenvir and the return value (the names of the createdobjects) is usually discarded.
See Also
Examples
## the objects are created with something like:ap <- pcts(AirPassengers)ap7to9 <- window(ap, seasons = 7:9)pcfr <- pcts(dataFranses1996)pcfr2to4 <- pcfr[2:4]Objects exported from other packages
Description
These objects are imported from other packages. Follow the linksbelow to see their documentation.
Functions for some basic operations with seasons
Description
Functions for some basic operations with seasons.
Usage
pdSafeParOrder(p)Arguments
p | autoregression order, a vector of integers. |
Details
pdSafeParOrder(p) modifies the periodic AR order specified by vectorp. The modified order is such that the correspondence betweenautocovariances and partial autocorrelations is one-to-one, seethe references for details.
Value
a vector of integers
Author(s)
Georgi N. Boshnakov
References
Lambert-Lacroix S (2000).“On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing,48( 6 ), pp. 1800-1803.
Lambert-Lacroix S (2005).“ Extension of autocovariance coefficients sequence for periodically correlatedprocesses.”Journal of Time Series Analysis,26(6), pp. 423-435.
Examples
pdSafeParOrder(c(0,2))pdSafeParOrder(c(2,3))McLeod's test for periodic autocorrelation
Description
Performs McLeod's test for periodic autocorrelation.
Usage
periodic_acf1_test(acf, nepochs)Arguments
acf | sample periodic autocorrelation function |
nepochs | the number of epochs used to get the acf |
Details
The test statistic is a scaled sum of squares of lag 1 sample periodicautocorrelation coefficients, see McLeod (1993), eq. (5). Thedistribution is approximately chi-square under the null hypothesis ofno periodic autocorrelation.
Value
A list containing the following components:
statistic | the value of the test statistic. |
pvalue | the p-value associated with the test statistic. |
Author(s)
Georgi N. Boshnakov
References
McLeod AI (1993).“Parsimony, model adequacy and periodic correlation in time series forecasting.”Internat. Statist. Rev.,61(3), 387-393.
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
McLeod AI (1995).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,16(6), 647-648.doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
Convert between periodic centering and intercepts
Description
Convert a periodic mean to periodic intercept and vice versa.
Usage
permean2intercept(mean, coef, order, nseasons = nrow(coef))intercept2permean(intercept, coef, order, nseasons = nrow(coef))Arguments
mean | periodic mean, numeric. |
coef | PAR coefficients, matrix. |
order | PAR order, vector of positive integers. |
nseasons | number of seasons, a.k.a. period. |
intercept | periodic intercepts, numeric. |
Details
A PAR model can be written in mean corrected or intercept form.permean2intercept calculates the intercepts from the means,whileintercept2permean does the inverse (means fromintercepts).
No check is made for periodic stationarity of the model. Convertingfrom mean corrected to intercept form allways succeeds and in fact themeans do not need to be means. In the opposite direction there may beproblems due to unit roots and similar features.
Value
a numeric vector
Author(s)
Georgi N. Boshnakov
Examples
mu <- c(1, 2)pm1 <- PeriodicArModel(matrix(c(0.5, 0.5), nrow = 2), order = rep(1, 2), sigma2 = 1, mean = mu)cc <- permean2intercept(mu, pm1@ar@coef, c(1,1))ccintercept2permean(cc, pm1@ar@coef, c(1,1))d <- 4mu <- 1:dco <- rep(0.5, d)pm1 <- PeriodicArModel(matrix(co, nrow = d), order = rep(1, d), sigma2 = 1, mean = mu)cc <- permean2intercept(mu, pm1@ar@coef, order = rep(1, d))ccintercept2permean(cc, pm1@ar@coef, order = rep(1, d) )Compute the multi-companion form of a per model
Description
Compute the multi-companion form of a per model.
Usage
permodelmf(permodel, update = TRUE)Arguments
permodel | a model. |
update | If TRUE store the multi-companion form in |
Details
todo:
Value
the multi-companion form of the model or the updated model, asdescribed in Details.
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
Convert PIAR coefficients to PAR coefficients
Description
Convert PIAR coefficients to PAR coefficients
Usage
pi1ar2par(picoef, parcoef)piar2par(picoef, parcoef)Arguments
picoef | coefficients of the periodic integration filter, anumeric vector or matrix, see Details. |
parcoef | coefficients of the periodically correlated part of the model. |
Details
These functions expand periodic filters represented in multiplicativeform. The non-periodic analogue of the operation of these functionsis representing a multiplicative filter like(1-B)(1-aB), whereB is the backward shift operator, by the single filter1 - (1+a)B + aB^2, which is just a product of the polynomials,1-Band1 - aB.
In the non-periodic case however this operation is not, in general,equivalent to multiplication of the corresponding polynomials. It isalso not commutative.
pi1ar2par converts PIAR(1) model coefficients specified as aset of coefficients corresponding to a periodic unit root and PARcoefficients to coefficients for a single filter.
piar2par does the same but admits higher order periodicintegration.
picoef is a matrix, specifying one or more first order periodicunit root filters. Each column contains the coefficients of onefilter. If there is only one filter, its coefficients can be given asa numeric vector.
The filters are applied from right to left, in the sense that firstthe PAR filter is applied to the time series, then the filterspecified by the last column and so on.
Value
a matrix, whose i-th row contains the coefficients for the i-th season.
Author(s)
Georgi N. Boshnakov
Examples
## Lina's exampleparcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) )picoef1 <- c(0.8, 1.25, 2, 0.5)parcoef2 <- pi1ar2par(picoef1, parcoef)picoef2 <- c(4, 0.25, 5, 0.2)coefper2I2 <- pi1ar2par(picoef2, parcoef2)McLeod-Ljung-Box test for periodic white noise
Description
Compute the McLeod-Ljung-Box test statistic for examiningthe null hypothesis of periodic white noise.
Usage
pwn_McLeodLjungBox_test(acf, nepoch, use = 1:maxlag, maxlag = ncol(as.matrix(acf)) - 1, period = nrow(as.matrix(acf)), fitdf = numeric(period))Arguments
acf | the sample periodic autocorrelation function of the time series. |
nepoch | number of cycles used in computing the acf. |
use | number of lags to use, may be a vector. |
maxlag | maximal lag. |
period | number of seasons in a cycle. |
fitdf | degrees of freedom corrections for the number ofestimated parameters, see Details. |
Details
The McLeod-Ljung-Box test can be used to test the null hypothesis ofperiodic white noise.
Ifacf contains sample autocorrelations of residuals from afitted model, a correction of the degrees of freedom is stronglyrecommended.
Argumentfitdf is a vector specifying how may degrees offreedom to subtract for each season. In the case of PAR modelsfitdf can be set to the PAR orders.
The value of the statistic is set to NA where the correction fordegrees of freedom results in negative numbers.
Value
A list containing the following components:
statistic | the value of the test statistic for each lagspecified by |
df | the corresponding degrees of freedom |
Note
TODO: Consolidate this and similar tests!
There is a typo in McLeod (1994), eq. (4.5),noted by (McLeod 1995).
Author(s)
Georgi N. Boshnakov
References
McLeod AI (1994).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,15(2), 221–233.
McLeod AI (1995).“Diagnostic checking of periodic autoregression models with application.”Journal of Time Series Analysis,16(6), 647-648.doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
See Also
Box.test for the non-periodic case
Methods for seqSeasons() in package pcts
Description
Methods for seqSeasons() in package pcts.
Methods
signature(x = "BasicCycle")signature(x = "Cyclic")signature(x = "VirtualPeriodicModel")
See Also
allSeasons for related functions and examples
Methods forsigmaSq in package pcts
Description
Methods forsigmaSq in package pcts.
Methods
signature(object = "PeriodicIntegratedArmaSpec")signature(object = "PeriodicInterceptSpec")
Create a random periodic autocovariance function
Description
Select randomly a periodic autoregression model and return theperiodic autocovariances associated with it.
Usage
sim_parAcvf(period, order, sigma2)Arguments
period | the period, a positive integer. |
order | the AR order, a vector of non-negative integers. |
sigma2 | the variances of the innovations, a numeric vector oflength |
Details
Usessim_parCoef() to generate a random PAR model.
Value
an object of class "matrix". In addition, the specification of themodel is in attribute"model" which is a list with thefollowing components:
ar | a matrix, the coefficients of the PAR model, |
sigma2 | numeric, the innovation variances, |
order | the PAR order. |
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
Examples
sim_parAcvf(2, 5)sim_parAcvf(3, 5)res <- sim_parAcvf(2, 6)resslMatrix(res)[3, 4, type = "tt"]res <- sim_parAcvf(2, 4)attr(res, "model")acv <- res[ , ] # drop attributesacv[2, 1 + 0]acv[2, 1 + 1]slMatrix(acv)[2, 0]slMatrix(acv)[2, 1]slMatrix(acv)[3, 4, type = "tt"]slMatrix(acv)[1:2, 1:2, type = "tt"]slMatrix(acv)[1:4, 1:4, type = "tt"]## TODO: need method for autocorrelation()## pc.acrf(acv)## TODO: these need changing, after the change of the return values of sim_parAcvf## pc.fcoeffs(acv, 2)## pc.fcoeffs(acv, 3)## pc.fcoeffs(acv, 4)pcts:::calc_predictionCoefficients(acv, c(2, 2))pcts:::calc_predictionCoefficients(acv, c(3, 3))pcts:::calc_predictionCoefficients(acv, c(4, 4))Generate a periodic autoregression model
Description
Generate a periodic autoregression model, possibly integrated.
Usage
sim_parCoef(period, n.root, sigma2 = rep(1, period), ...)Arguments
period | number of seasons in a cycle. |
n.root | number of non-zero roots, see details. |
sigma2 | variances of the innovations. |
... | additional arguments to be passed down to |
Details
sim_parCoef uses the multi-companion method to generate themodel. The function is essentially a wrapper forsim_pcfilter.
The order of the filter is set ton.root for each season. Partof the spectral information may be specified with the"..."arguments, seesim_pcfilter andsim_mc fora discussion of this.
Value
a periodic autoregression model as a list with elements:
ar | a matrix whose |
sigma2 | the innovation variances, a numeric vector. |
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
See Also
Examples
sim_parCoef(2, 4) # 2 seasonssim_parCoef(2, 4, sigma2 = c(2, 4))sim_parCoef(2, 1)sim_parCoef(4, 2) # 4 seasonssim_parCoef(period = 4, n.root = 6, eigabs = c(1, 1, 1, 0.036568887, 0.001968887), type.eigval = c("cp", "r", "r", "r", "r"), eigsign = c(pi/2, 1, -1, 1, -1))Simulate periodically correlated ARMA series
Description
Simulate a realization of a periodically correlated arma modelor a continuation of an existing series.Initial values may be given too.
Usage
sim_pc(model, n = NA, randgen = rnorm, seasonof1st = 1, nepochs = NA, n.start = NA, x, eps, nmean = NULL, nintercept = NULL, ...)Arguments
model | a list with elements |
n | length of the series. |
randgen | random number generator as required by |
seasonof1st | season of the first value. |
nepochs | number of epochs; if |
n.start | burn-in number; generate |
x | initial orbefore values, see Details. |
eps | innovations, see Details. |
nmean | a vector of length |
nintercept | a vector of length |
... | any additional arguments to be passed on to |
Details
Argumentx can be used to specify two types of initialisationvalues - ‘before’ and ‘init’. They are used similarly in computationsbut ‘before’ values are not included in the result, while ‘init’values are (unless dropped due ton.start). ‘Before’ valuesprovide a convenient way to simulate continuation trajectories for atime series, for example for simulation based prediction intervals.
Ifx is"numeric", it represents ‘before’values. Alternatively,x can be a list with components"before" and"init".
Innovations are usually generated with the random number generatorspecified byrandgen (with defaultrnorm) and the... parameters by a call to the functionsim_pwn, seethe documentation forsim_pwn for various ways to control thedistribution of the generated sequence.
The innovations can also be generated in advance and supplied usingargumenteps. Ifeps is numeric, it is taken torepresent the innovations. Alternatively,eps can be a listwith the innovations in component"main". This list may alsocontain components"before" and/or"init" specifying‘before’ or ‘initial’ values, with interpretation as forx.
nintercept can be used to specify trend representing the effectof time and/or covariates. As foreps, if it is numeric it istaken to represent the main values. It can also be a list withcomponentsbefore,init, andmain.
To avoid ambiguity, let's reiterate thatbefore values are pastvalues of the corresponding quantity (before the start of thesimulated series), whileinit values are "initial" values. Inparticular, if initial values are specified forx, these willform the start of the generated series (unlessn.start leads tothem being discarded).
Ifbefore values are specified for the series and theinnovations, then they play a role analogous to that of initialvalues, so it does not make much sense to supply alsoinitialvalues.
The function effectively does the following.innov is generated if not supplied,a vector of innovations is createdeps <- c(innovbefore,innovinit,innov),a vectorx is created of the same length aseps,and initialised withxbefore andxinit.If there are no initial or before values, these are assumed to be 0.The remaining values ofx are filled using the pc-arma equations.Finally, thexbefore values are discarded as well as the firstn.start values.
n.start should usually be a multiple of the period sinceotherwise the first observation in the returned vector will notcorrespond toseasonof1st.
sim_pc deals mainly with the interpretation of the parameters.The actual computations are done bypc.filter. Moreover,sim_pc does not look at themodel. It knows only aboutmodel$period and uses it to computen ifn is notspecified.(It probably should not care even about this.)
Value
numeric, the simulated time series
To do
option to return the innovation sequence;option to include the before values.
option to return the season of the first value in the returned series(it may be different from seasonof1st due ton.start).
Author(s)
Georgi N. Boshnakov
See Also
Examples
m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )testphi <- slMatrix( init = m1 )m2 <- rbind( c(1, 0, 0), c(1, 0, 0) )testtheta <- slMatrix( init = m2 )## phi and theta are slMatrix here.mo1 <- list(phi = testphi, theta = testtheta, p = 2, q = 2, period = 2)set.seed(1234)a1 <- sim_pc(mo1, 100)## phi and theta are ordinary matrices here.mo2 <- list(phi = m1[ , 2:ncol(m1)], theta = m2[ , 2:ncol(m2)], p = 2, q = 2, period = 2)set.seed(1234)a2 <- sim_pc(mo2, 100)identical(a1, a2)## Lina's PAR modelparcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) )picoef1 <- c(0.8, 1.25, 2, 0.5)parcoef2 <- pi1ar2par(picoef1, parcoef)picoef2 <- c(4, 0.25, 5, 0.2)coefper2I2 <- pi1ar2par(picoef2, parcoef2)#### specify the model using multi-companion approachmc2I2 <- mcompanion::mc_from_filter(coefper2I2)co2I2 <- eigen(mc2I2)$vectorsco2I2m2I2 <- mcompanion::sim_pcfilter(period = 4, n.root = 4, eigabs = c(1, 0.036568887, 0.001968887), eigsign = c(1, 1, -1), len.block = c(2, 1, 1), type.eigval = c("r", "r", "r"), co = cbind(co2I2[ ,1], rep(NA, 4), co2I2[,3:4]))m2I2$pcfilterperunit2mc <- sim_pc(list(phi = m2I2$pcfilter, p = 4, q = 0, period = 4), 500)plot(perunit2mc)plot(perunit2mc, type = "p")# todo: give example with sigmat^2 !!!Simulate periodic white noise
Description
Simulate periodic white noise.
Usage
sim_pwn(n = 100, period = NA, seasonof1st = 1, scale = NULL, shift = NULL, f = rnorm, ...)Arguments
n | length of the generated sample. |
period | number of seasons in an epoch. |
seasonof1st | season of the first observation in the result. |
scale | scale the series by this amount, a vector of length |
shift | shift the series by this amount, a vector of length |
f | a function or list of functions to generate random numbers. |
... | arguments for the random number generator(s) specified by |
Details
First a series, sayx, of random numbers is generated asrequested by the argumentf. Then, ifshift and/orscale are supplied, the values are modified as follows:
y_t = shift_{k} + scale_{k} x_t
wherek is the season corresponding to timet.The vectory is returned.
Iff is a single a function (or name of a function), then theseries is generated (effectively) by the callf(n,...).
The argumentf may also be a list whosekth elementis itself a list specifying the random number generator for thekth season. The first element being the function (such asrnorm) and the remaining elements being parameters for thatfunction. Parameters common to all seasons may be supplied throughthe ... argument.
The argumentperiod may be omitted. In that case it is inferredfromf and/or the lengths ofshift andscale. Currently there is no check for consistency here.
The argumentsshift andscale may be used to specifysimple linear transformations of the generated values, possiblydifferent for the different seasons. Each of them should be a vectorof lengthperiod or one.
seasonof1st can be used to request the simulated time series tostart from a season other than the first one. Note that whatever thevalue ofseasonof1st, the first elements ofscale,shift andf (if a list) are taken to refer to seasonone.
Value
A vector of lengthn representing a realization of a periodicwhite noise series. The season of the first observation isseasonof1st.
Level
0 (base)
Author(s)
Georgi N. Boshnakov
Examples
## three equivalent ways to specify periodic white noise with## normal innovatios, 2 seasons, s.d. = 0.5 for season 1, and 2 for season 2sim_pwn(100, f = rnorm, scale = c(0.5, 2))sim_pwn(n = 100, scale = c(0.5, 2)) # rnorm is the default generatorsim_pwn(100, f = list(c(rnorm, 0, 0.5), c(rnorm, 0, 2)))Functions for some basic operations with seasons
Description
Functions for some basic operations with seasons.
Usage
toSeason(t, period, t1 = 1, from = 1)toSeasonPair(t, s, period, ...)ttTosl(r, period)ttmatToslPairs(i, j, period)Arguments
r | covariance matrix, see ‘Details’. |
t | a vector of integers, representing times. |
s | a vector of integers, representing times. |
period | the number of seasons. |
t1 | time corresponding to the first season, an integer number. |
from | 1 or 0, depending on whether the season numbers start from1 or 0. |
i | a vector of integers. |
j | a vector of integers. |
... | todo: describe! |
Details
ttmatToslPairs(i,j,period) transforms time-time pairs toseason-lag pairs. The time pairs are obtained by pairing each elementofi with each element ofj. A four column matrix iscreated with one row for each pair(t,s), such thatt=i[m] ands=j[n] for somem andn. Therow ism, n, s, l, where(s,l) is the season-lag paircorresponding to(t,s).
ttTosl(r,period) converts autocovariances given in a covariancematrix (i.e. in “tt” form) to the “sl” form. The result is aperiod x (maxlag+1) matrix, wheremaxlag is the maximallag available inr. Entries for which no values are availableare filled withNA's. Warning is given if contradictory entriesare found (i.e. ifr is not from a periodically correlatedprocess with the given period).
toSeason(t,period,t1=1,from=1) returns the season correspondingtot.t1 is a time (integer) whose season is the firstseason,from is 1 if the numbering of seasons is 1,2,...,period,or 0 if the numbering of seasons is 0,1,...,period-1. Other values forfrom are not admissible (but not checked).Note: someof the functions in this package implicitly assume thatt1=1 andfrom=1.
toSeasonPair(t,s,period) converts the “tt” pairt,s to“sl” pair and returns the result in the form of a list with elementsseason andlag. Currentlyt ands must bescalars.
pc.omitneg helps to implement dropping of negative indices inseason-lag objects. It returns its first argument,lags, if allof its elements are non-negative. Otherwise, all elements oflags must be non-positive. In this case the function creates thevector0:maxlag and drops the elements specified by lags. Notethat the default indexing will not work properly since zero elements inan index are omitted (and there are such indices in season-lagobjects).
Value
forttmatToslPairs, a matrix with four columns;
forttTosl, a matrix withperiod rows;
fortoSeason(t,period,t1=1,from=1), a vector of integers;
fortoSeasonPair(t,s,period), a list with elementsseason andlag;
forpc.omitneg, a vector of lags (non-negative integers).
Note
2013-10-24 - Corrected the description of the return value ofttmatToslPairs. It incorrectly stated that the first twocolumns are "tt" pair (they are actually indices ini andj).
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN, Iqelan BM (2009).“Generation of time series models with given spectral properties.”J. Time Series Anal.,30(3), 349–368.ISSN 0143-9782,doi:10.1111/j.1467-9892.2009.00617.x.
Examples
# ttmatToslPairsttmatToslPairs(3, 3, 4) # 1, 1, 3, 0ttmatToslPairs(3, 2, 4) # 1, 1, 3, 1ttmatToslPairs(1:4, 1:4, 4)ttmatToslPairs(3:4, 3:4, 4)# ttTosl - :todo:# toSeasontoSeason(1:10, 4) # 1 2 3 4 1 2 3 4 1 2toSeason(1:10, 4, from = 0) # 0 1 2 3 0 1 2 3 0 1## first data is for 3rd quartertoSeason(1:10, 4, t1 = 3) # 3 4 1 2 3 4 1 2 3 4# toSeasonPairtoSeasonPair(3, 3, period=4) # season=3, lag = 0toSeasonPair(8, 8, period=4) # season=4, lag = 0toSeasonPair(3, 2, period=4) # season=3, lag = 1toSeasonPair(7, 6, period=4) # same#### # pc.omitneg#### pc.omitneg(0:5,10) # 0:5, unchaged since all values >= 0#### #### pc.omitneg(-(0:5),10) # 6:10, works like#### (0:10)[-(0:5 +1)] # same#### #### # don't mix positive and negative numbers in pc.omitneg#### \dontrun{pc.omitneg(c(0,2,3,-4,5), 10)}Methods for function tail() in package pcts
Description
Methods for function tail() in package pcts.
Methods
signature(x = "PeriodicTimeSeries")
Test for periodic integration
Description
Test if a time series is periodically integrated.
Usage
test_piar(x, d, p, sintercept = FALSE, sslope = FALSE, homoschedastic = FALSE)Arguments
x | time series. |
d | period. |
p | autoregressive order, a positive integer. |
sintercept | if TRUE, include seasonal intercept. |
sslope | if TRUE, include seasonal slope. |
homoschedastic | if TRUE, assume the innovations variance is thesame for all seasons. |
Details
Computes test statistics for Franses (1996) test for periodicintegration of order 1. The test is based on periodic autoregressionof orderp, wherep can be any positive integer.
Value
a list with the following components:
p | autoregressive order. |
spec | values of |
statistics | a matrix containing the test statistics (first row) and thecorresponding p-values (second row). |
Note
Currently only the casep = 1 is handled, forp > 1 thestatistics are set to NA.:TODO: handle this.
All statistics are computed but some p-values are not computed yet.
Author(s)
Georgi N. Boshnakov
References
Boswijk HP and Franses PH (1996).“Unit roots in periodic autoregressions.”Journal of Time Series Analysis,17(3), pp. 221–245.
See Also
Examples
ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4))test_piar(ts1, 4, 1, sintercept = TRUE)pcTest(ts1, "piar", 4, 1, sintercept = TRUE) # sametest_piar(ts1, 4, 1, sintercept = TRUE, sslope = TRUE)test_piar(ts1, 4, 1) test_piar(ts1, 4, 1, homoschedastic = TRUE)Methods for`unitCycle<-` and`unitSeason<-` in package pcts
Description
Methods for`unitCycle<-` and`unitSeason<-`in package pcts.
Methods
`unitCycle<-` and`unitSeason<-` have methods with identicalsignatures:
signature(x = "Cyclic")signature(x = "SimpleCycle")
See Also
allSeasons for related functions and examples
Examples
qrt <- BuiltinCycle(4)unitSeason(qrt) # "Quarter"unitCycle(qrt) # "Year"moreve <- new("SimpleCycle", 2)unitSeason(moreve) # "Season"unitCycle(moreve) # "Cycle"allSeasons(moreve) # c("Season_1", "Season_2")## change the namesunitCycle(moreve) <- "Day"unitSeason(moreve) <- "TimeOfDay"allSeasons(moreve) <- c("Morning", "Evening")unitSeason(moreve)unitCycle(moreve) allSeasons(moreve)Methods forunitCycle andunitSeason in package pcts
Description
Methods forunitCycle andunitSeason in package pcts.
Methods
unitCycle andunitSeason have methods with identicalsignatures:
signature(x = "ANY")signature(x = "VirtualPeriodicModel")signature(x = "Cyclic")signature(x = "SimpleCycle")signature(x = "PartialCycle")signature(x = "OpenCloseCycle")signature(x = "QuarterYearCycle")signature(x = "DayWeekCycle")signature(x = "MonthYearCycle")signature(x = "Every30MinutesCycle")
See Also
allSeasons for examples and related functions
Examples
## presidents is a quarterly time series in base-Rtsp(presidents)pc_presidents <- pcts(presidents)unitCycle(pc_presidents)unitSeason(pc_presidents)Periodic methods for base R functions
Description
Periodic methods for base R functions.
Usage
## S3 method for class 'PeriodicTS'window(x, start = NULL, end = NULL, seasons = NULL, ...)## S3 method for class 'PeriodicMTS'window(x, start = NULL, end = NULL, seasons = NULL, ...)## S3 method for class 'PeriodicTS'na.trim(object, sides = c("both", "left", "right"), ...)## S3 method for class 'PeriodicMTS'na.trim(object, sides = c("both", "left", "right"), is.na = c("any", "all"), ...)## S3 method for class 'PeriodicTimeSeries'frequency(x, ...)## S3 method for class 'PeriodicTimeSeries'deltat(x, ...)## S3 method for class 'PeriodicTimeSeries'cycle(x, ...)## S3 method for class 'PeriodicTimeSeries'time(x, offset = 0, ...)## S3 method for class 'Cyclic'start(x, ...)## S3 method for class 'Cyclic'end(x, ...)Arguments
x,object | an object from the indicated periodic class. |
start |
|
end |
|
seasons | numeric, a subset of |
... | Not used by these methods. |
sides | which side to trim: start ( |
is.na | for multivariate time series: if |
offset | currently ignored (:TODO:) |
Details
Periodic methods for base R and other common functions formanipulation of time series. These methods work analogoulsly to theirbase R cousins and only the differences, if any, are discussed below.
window takes a part ofx, preserving theclass of the object. Argumentseasons selects a subset of theseasons.
na.trim is a function defined in packagezooand re-exported bypcts. It trimsNAs from one or bothends of the time series, as requested by the arguments. The argumentsof the methods defined bypcts have the same meaning as those inzoo.
Value
forwindow andna.trim, an object from the same class as the original, representing therequested part of the time series.
forfrequency, an integer number.
fordeltat, a number (1/frequency).
forcycle andtime, a"PeriodicTS" object.
forstart andend, time of first/last observation,encoded as a pair of numbers.
See Also
window,frequency,na.trim for details on what these functions do.
availStart andavailEnd give the times ofthe first and last non-NA observations.
Examples
pres <- pcts(presidents)head(pres, 8)availStart(pres)tail(pres, 12)availEnd(pres)## Q3 and Q4 onlypresQ3Q4 <- window(pres, seasons = 3:4)head(presQ3Q4)identical(na.trim(pres), window(pres, start = availStart(pres), end = availEnd(pres)))## TRUEClass zoo made S4
Description
Class zoo made S4
Objects from the Class
A virtual Class: No objects may be createdfrom it.
S4 Class"zoo" is derived from its namesake in packagezoo for use as a super class for periodic time series classesand in S4 method signatures.
Slots
.S3Class:Object of class
"character"~~
Extends
Class"oldClass", directly.
Methods
No methods defined with class "zoo" in the signature.
See Also
PeriodicTS_zooreg,zooregand packagezoo
Examples
showClass("zoo")Virtual S4 class zooreg
Description
Virtual S4 class zooreg.
Objects from the Class
A virtual Class: No objects may be createdfrom it.
S4 Class"zooreg" is derived from its namesake in packagezoo for use as a super class for periodic time series classesand in S4 method signatures.
Slots
.S3Class:Object of class
"character"~~
Extends
Class"zoo", directly.Class"oldClass", by class "zoo", distance 2.
Methods
No methods defined with class "zooreg" in the signature.
See Also
PeriodicTS_zooreg,zooand packagezoo
Examples
showClass("zooreg")