| Version: | 0.1.1 |
| Title: | Time Series Cointegrated System |
| Maintainer: | Tianjian Yang <yangtj5@mail2.sysu.edu.cn> |
| Description: | A set of functions to implement Time Series Cointegrated System (TSCS) spatial interpolation and relevant data visualization. |
| Depends: | R (≥ 3.4.2) |
| Imports: | stats, ggplot2 (≥ 2.2.1), tseries (≥ 0.10-42), rgl (≥0.98.1), grDevices |
| License: | GPL-2 |GPL-3 [expanded from: GPL (≥ 2.0)] |
| RoxygenNote: | 6.0.1 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Suggests: | knitr, rmarkdown, R.rsp |
| VignetteBuilder: | knitr, R.rsp |
| NeedsCompilation: | no |
| Packaged: | 2017-10-02 11:11:52 UTC; MSI |
| Author: | Tianjian Yang [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2017-10-02 11:19:48 UTC |
A Package for TSCS Spatial Interpolation Method
Description
This package provides functions to implement TSCS spatial interpolation andrelevant data visualization. For TSCS method, the current version is only able tomake use of spatio-temporal data whose spatial domain is a 2D or 3D rectangular grid system.
Details
TSCS (abbr. of Time Series Cointegrated System) method is a spatialinterpolation method based on analysis of historical spatio-temporal data.It can be regarded as a desirable alternative to spatio-temporal interpolationin some cases where we merely intend to interpolate a series of cross-section dataat each observed time point for a given spatial domain.
The basic assumption of TSCS method is that, for any spatial location withinthe spatial domain of spatio-temporal data, its time series and the time series ofits adjacent spatial locations are cointegrated (long-term equilibrium relationships).
As to TSCS method, package of the current version is only able to make use ofspatio-temporal data whose spatial domain is a 2D or 3D rectangular grid system.
Package Functions
tscsRegression, tscsRegression3D: obtains regression coefficient matrix, the first step ofTSCS for 2D and 3D rectangular grid system respectively.tscsEstimate, tscsEstimate3D: estimates the missing observations within a cross-section data(pure spatial data) of a particular time point you have selected, the second step of TSCS for 2D and 3Drectangular grid system respectively.plot_dif, plot3D_dif: differentiates boundary and interior spatial locations in a spatial domain.plot_NA, plot3D_NA: shows spatial locations with or without missing observation in a spatial domain.plot_map, plot3D_map: draws the spatial map for a cross-section data.plot_compare: visualizes the comparison between estimates and true values (if you have).appraisal_index: computes the two appraisal indexes used for evaluating the result ofinterpolation/prediction - RMSE and standard deviation of error. (if you have the true values)
Author(s)
Tianjian Yang <yangtj5@mail2.sysu.edu.cn>
Compute Appraisal Index of Interpolation/Prediction Result
Description
Two appraisal indexes used for evaluating the result of interpolation/prediction - RMSE andstandard deviation of error.
Usage
appraisal_index(est, true)Arguments
est | a numeric vector; estimations. |
true | a numeric vector; true values. |
Details
The first appraisal index is RMSE, abbr. of root-mean-square error. It is used for measuring the differencesbetween estimated values by a method and the values actually observed. Smaller RMSE means more accurateinterpolation/prediction.
The second appraisal index is standard deviation of error, which is used for measuring how far the errorsare spread out from their mean, namely, stability of errors. Smaller value means greater stability of errors,suggesting that errors would not fluctuate heavily due to difference of data.
Value
A list of 2 is returned, including:
RMSEnumeric; RMSE.
stdnumeric; standard deviation of error.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)Visualize the Spatial Distribution of Missing Observations - 3D Map
Description
plot3D_NA shows spatial locations with or without missing observation. It is plotted based onthe cross-section data of a given time point, which is also often extracted from spatio-temporal data.
Usage
plot3D_NA(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3, color = "orange", colorNA = "blue")Arguments
newdata | data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinateand observation. This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
zlab | a label for the z axis, defaults to the name of Z coordinate. |
title | a main title for the plot. |
cex | numeric; size of plotting point for each spatial location. (default: 3) |
color | colour to be used to fill the spatial locations. (default: "orange") |
colorNA | colour for denoting missing values/observations. (default: "blue") |
Details
The resulting plot is interactive.
plot3D_NAis exclusive to 3D rectangular grid system. Similarly, if you want to fathom howthis package handles 2D rectangular grid system, please refer toplot_NA.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01);basis$percentageest <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5);str(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,4], true = true)index <- appraisal_index(est = est$estimate[,4], true = true);index## data visualization:plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5)plot3D_NA(newdata = newdata)plot3D_map(newdata = newdata)## End(Not run)Plot Interior Spatial Locations and System Boundary - 3D Map
Description
plot3D_dif differentiates boundary and interior spatial locations in a spatial domain (a collection ofspatial locations with their coordinates). Since TSCS method is only capable of interpolation but notextrapolation, it is necessary to highlight the difference between interior spatial locations and system boundary.
Usage
plot3D_dif(coords, h1, h2, v, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3)Arguments
coords | data frame; should only contain the three variables: X coordinate, Y coordinate and Z coordinate.Each row uniquely denotes a spatial location. (coordinates must be numeric) |
h1 | numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 | numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v | numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
zlab | a label for the z axis, defaults to the name of Z coordinate. |
title | a main title for the plot. |
cex | numeric; size of point to be plotted for each spatial location. (default: 3) |
Details
The resulting plot is interactive, where the red points are interior spatial locationswhile the black points denote system boundary.
plot3D_difis exclusive to 3D rectangular grid system. Similarly, if you want to fathom howthis package handles 2D rectangular grid system, please refer toplot_dif.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01);basis$percentageest <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5);str(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,4], true = true)index <- appraisal_index(est = est$estimate[,4], true = true);index## data visualization:plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5)plot3D_NA(newdata = newdata)plot3D_map(newdata = newdata)## End(Not run)Visualize Spatial(Cross-Section) Data of a Given Time Point - 3D Map
Description
plot_map draws a three-dimensional spatial map. It is plotted based on the cross-section dataof a given time point, which is also often extracted from spatio-temporal data.
Usage
plot3D_map(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 9, colorNA = "white")Arguments
newdata | data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinateand observation. This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
zlab | a label for the z axis, defaults to the name of Z coordinate. |
title | a main title for the plot. |
cex | numeric; size of plotting point for each spatial locations. (default: 9) |
colorNA | colour for missing values/observations. (default: "white") |
Details
The resulting plot is interactive.
plot3D_mapis exclusive to 3D rectangular grid system. Similarly, if you want to fathom howthis package handles 2D rectangular grid system, please refer toplot_map.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01);basis$percentageest <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5);str(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,4], true = true)index <- appraisal_index(est = est$estimate[,4], true = true);index## data visualization:plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5)plot3D_NA(newdata = newdata)plot3D_map(newdata = newdata)## End(Not run)Visualize the Spatial Distribution of Missing Observations - 2D Map
Description
plot_NA shows spatial locations with or without missing observation. It is plotted based onthe cross-section data of a given time point, which is also often extracted from spatio-temporal data.
Usage
plot_NA(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 1)Arguments
newdata | data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation.This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
title | a main title for the plot. |
cex | numeric; size of plotting point for each spatial location. (default: 1) |
Details
plot_NA is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this packagehandles 3D rectangular grid system, please refer toplot3D_NA.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)Graphic Comparison Between Estimates and True Values
Description
Provided that you have the true values of missing observations, you can compare themwith the results of interpolation.plot_compare visualizes the comparisonbetween estimates and true values. (NB: this plotting function can also be usedin other similar situations involving comparison between estimates and true values.)
Usage
plot_compare(est, true, cex = 1, width = 1, P = 6/7, AI = TRUE)Arguments
est | a numeric vector; estimations. |
true | a numeric vector; true values. |
cex | numeric; size of point to be plotted. (default: 1) |
width | numeric; width of fitted straight line. (default: 1) |
P | numeric, between 0 and 1; position for superimposing values of appraisal indexes. (default: 6/7) |
AI | logical; |
Details
Attentions:
The values in
estandtruevectors should be arranged in the same order,in correspondence with the sequence of observations.If the maximum value of either
estortrueis greater than 1000, or theminimum is smaller than -1000, please make appropriate transformation that limits your datato bound [-1000,1000].
In the plot:
The big red point is the origin.
The red line stands for straight line
y = x.The blue line stands for fitted straight line.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01) # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1) # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)Plot Interior Spatial Locations and System Boundary - 2D Map
Description
plot_dif differentiates boundary and interior spatial locations in a spatial domain (a collection ofspatial locations with their coordinates). Since TSCS method is only capable of interpolation but notextrapolation, it is necessary to highlight the difference between interior spatial locations and system boundary.
Usage
plot_dif(coords, h, v, xlab = NULL, ylab = NULL, title = NULL, cex = 1)Arguments
coords | data frame; should only contain the two variables: X coordinate and Y coordinate. Each row uniquelydenotes a spatial location. (coordinates must be numeric) |
h | numeric; side length of the unit grid in X coordinate direction. |
v | numeric; side length of the unit grid in Y coordinate direction. |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
title | a main title for the plot. |
cex | numeric; size of plotting point for each spatial location. (default: 1) |
Details
plot_dif is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this packagehandles 3D rectangular grid system, please refer toplot3D_dif.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)Visualize Spatial(Cross-Section) Data of a Given Time Point - 2D Map
Description
plot_map draws a two-dimensional spatial map. It is plotted based on the cross-section dataof a given time point, which is also often extracted from spatio-temporal data.
Usage
plot_map(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 2, shape = 15, low = "blue", mid = "yellow", high = "red", na.value = "white", midpoint = NULL)Arguments
newdata | data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation.This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
xlab | a label for the x axis, defaults to the name of X coordinate. |
ylab | a label for the y axis, defaults to the name of Y coordinate. |
title | a main title for the plot. |
cex | numeric; size of plotting point for each spatial locations. (default: 2) |
shape | either an integer specifying a symbol or a single character to be used as the defaultin plotting points. (default: 15) |
low,high | colours for low and high ends of the gradient. (default: "blue","red") |
mid | colour for midpoint of the gradient. (default: "yellow") |
na.value | colour for missing values/observations. (default: "white") |
midpoint | numeric; the midpoint of the gradient scale, defaults to the midpoint value of index presented. |
Details
plot_map is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this packagehandles 3D rectangular grid system, please refer toplot3D_map.
See Also
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)The Second Step of TSCS for 2D Rectangular Grid System - Estimation
Description
tscsEstimate estimates the missing observations within the cross-section data (pure spatial data)of a particular time point you have selected, namely, the interpolation process.
Usage
tscsEstimate(matrix, newdata, h, v)Arguments
matrix | data frame; the first return value |
newdata | data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation.This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
h | numeric; side length of the unit grid in X coordinate direction. |
v | numeric; side length of the unit grid in Y coordinate direction. |
Details
The first step of TSCS spatial interpolation should be carried out by function
tscsRegression,which is the prerequisite oftscsEstimate.For 3D rectangular grid system, the procedure of TSCS stays the same.Please see
tscsRegression3DandtscsEstimate3D.Attentions:Since TSCS is only capable of interpolation but not extrapolation, please make sure thatthe missing observations in a given spatial domain are all located at interior spatial locations.Otherwise, extrapolation would occur with an error following.
Value
A list of 3 is returned, including:
estimatedata frame; estimate of missing observations which contains the 3 variables in order:X coordinate, Y coordinate and estimation.
completedata frame; an updated version of the cross-section data (pure spatial data)
newdata,with all of its missing observations interpolated.NA_idan integer vector; reveals the instance ID, in data frame
newdata,of spatial locations with missing observation.
See Also
tscsRegression,tscsEstimate3D,plot_NA,plot_map
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)The Second Step of TSCS for 3D Rectangular Grid System - Estimation
Description
tscsEstimate estimates the missing observations within the cross-section data (pure spatial data)of a particular time point you have selected, namely, the interpolation process.
Usage
tscsEstimate3D(matrix, newdata, h1, h2, v)Arguments
matrix | data frame; the first return value |
newdata | data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinateand observation. This is the cross-section data or pure spatial data of a particular time point you have selected,with missing observations that you want to predict. (coordinates must be numeric) |
h1 | numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 | numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v | numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
Details
The first step of TSCS spatial interpolation should be carried out by function
tscsRegression3D,which is the prerequisite oftscsEstimate3D.For 2D rectangular grid system, the procedure of TSCS stays the same.Please see
tscsRegressionandtscsEstimate.Attentions:Since TSCS is only capable of interpolation but not extrapolation, please make sure thatthe missing observations in a given spatial domain are all located at interior spatial locations.Otherwise, extrapolation would occur with an error following.
Value
A list of 3 is returned, including:
estimatedata frame; estimate of missing observations which contains the 4 variables in order:X coordinate, Y coordinate, Z coordinate and estimation.
completedata frame; an updated version of the cross-section data (pure spatial data)
newdata,with all of its missing observations interpolated.NA_idan integer vector; reveals the instance ID, in data frame
newdata,of spatial locations with missing observation.
See Also
tscsRegression3D,tscsEstimate,plot3D_NA,plot3D_map
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01);basis$percentageest <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5);str(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,4], true = true)index <- appraisal_index(est = est$estimate[,4], true = true);index## data visualization:plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5)plot3D_NA(newdata = newdata)plot3D_map(newdata = newdata)## End(Not run)The First Step of TSCS for 2D Rectangular Grid System - Regression
Description
To implement TSCS spatial interpolation for a spatial domain that is a 2D rectangular grid system,the first step is obtaining regression coefficient matrix, which can be doneby functiontscsRegression. It is the prerequisite of TSCS interpolation processbecause the 'matrix' derived from historical spatio-temporal data is the initial value ofthe second step - estimating missing observations.
Usage
tscsRegression(data, h, v, alpha = 0.05)Arguments
data | data frame; should contain these variables in order: X coordinate, Y coordinate and observationsas time goes on. That is to say, each row should include X and Y coordinate first, and then a time series.This is the historical spatio-temporal data that you intend to analyze as the basis forinterpolation later on in |
h | numeric; side length of the unit grid in X coordinate direction. |
v | numeric; side length of the unit grid in Y coordinate direction. |
alpha | numeric; specify the significance level for ADF test, to test if the time series of a group ofspatial locations are cointegrated. (default: 0.05) |
Details
The second step of TSCS spatial interpolation should be carried out by function
tscsEstimate,where you have to input the cross-section data or pure spatial data of a particular time pointyou have selected, with missing observations that you want to predict.For 3D rectangular grid system, the procedure of TSCS stays the same.Please see
tscsRegression3DandtscsEstimate3D.Attentions:(1) Since TSCS is only capable of interpolation but not extrapolation, it is necessary to highlight thedifference between interior spatial locations and system boundary. Function
plot_difcan help.(2) NA value in historical spatio-temporal datadatais not allowed. Please handle them beforehand(such as filling these NA values through spatio-temporal kriging).
Value
A list of 2 is returned, including:
coef_matrixdata frame; regression coefficient matrix to be used as input parameter of function
tscsEstimatein the second step of TSCS interpolation.percentagenumeric; percentage of cointegrated relationships, a measurement of the degreeit satisfies the assumption of cointegrated system. It is highly affected by parameter
alpha,the significance level you have set. Explicitly, smalleralpharesults in smallerpercentage.
See Also
tscsEstimate,tscsRegression3D,plot_dif
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regressionbasis$percentage # see the percentage of cointegrated relationshipsest <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimationstr(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,3], true = true) # graphic comparisonindex <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & stdindex## data visualization:plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locationsplot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section dataplot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data## End(Not run)The First Step of TSCS for 3D Rectangular Grid System - Regression
Description
To implement TSCS spatial interpolation for a spatial domain that is a 3D rectangular grid system,the first step is obtaining regression coefficient matrix, which can be doneby functiontscsRegression3D. It is the prerequisite of TSCS interpolation processbecause the 'matrix' derived from historical spatio-temporal data is the initial value ofthe second step - estimating missing observations.
Usage
tscsRegression3D(data, h1, h2, v, alpha = 0.05)Arguments
data | data frame; should contain these variables in order: X coordinate, Y coordinate, Z coordinate andobservations as time goes on. That is to say, each row should include X, Y and Z coordinate first, and thena time series. This is the historical spatio-temporal data that you intend to analyze as the basis forinterpolation later on in |
h1 | numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 | numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v | numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
alpha | numeric; specify the significance level for ADF test, to test if the time series of a group ofspatial locations are cointegrated. (default: 0.05) |
Details
The second step of TSCS spatial interpolation should be carried out by function
tscsEstimate3D,where you have to input the cross-section data or pure spatial data of a particular time pointyou have selected, with missing observations that you want to predict.For 2D rectangular grid system, the procedure of TSCS stays the same.Please see
tscsRegressionandtscsEstimate.Attentions:(1) Since TSCS is only capable of interpolation but not extrapolation, it is necessary to highlight thedifference between interior spatial locations and system boundary. Function
plot3D_difcan help.(2) NA value in historical spatio-temporal datadatais not allowed. Please handle them beforehand(such as filling these NA values through spatio-temporal kriging).
Value
A list of 2 is returned, including:
coef_matrixdata frame; regression coefficient matrix to be used as input parameter of function
tscsEstimatein the second step of TSCS interpolation.percentagenumeric; percentage of cointegrated relationships, a measurement of the degreeit satisfies the assumption of cointegrated system. It is highly affected by parameter
alpha,the significance level you have set. Explicitly, smalleralpharesults in smallerpercentage.
See Also
tscsEstimate3D,tscsRegression,plot3D_dif
Examples
## Not run: ## TSCS spatial interpolation procedure:basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01);basis$percentageest <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5);str(est)## comparison of estimates and true values:plot_compare(est = est$estimate[,4], true = true)index <- appraisal_index(est = est$estimate[,4], true = true);index## data visualization:plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5)plot3D_NA(newdata = newdata)plot3D_map(newdata = newdata)## End(Not run)