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[character(1)]
The date in format"YYYY-MM-DD".

A list of one or more objects of classfHMM_model.

The elementcontrols$horizon, i.e., an integer vector of length 2,where the second entry can beNA_integer_.

The elementcontrols$period, i.e. one of"w","m","q", or"y".

Acharacter vector of dates of empirical fine-scale data (if any).By default,dates = NULL.

Set a seed for the simulation of flexible chunk lengths.By default,seed = NULL (i.e., no seed).

An object of classfHMM_model.

Anumeric between 0 and 1, the alpha level for the confidence interval.By default,alpha = 0.05, which computes a 95% confidence interval.

An object of classfHMM_model.

Set toTRUE (default) to print progress messages.

An object of classfHMM_model.

Set toTRUE to print progress messages.

Anumericvector of state-dependent observations.

The number of states.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

A transition probabilitymatrix of dimensionnstates.

Anumeric vector of expected values for the state-dependentdistribution in the different states of lengthnstates.

For the gamma- or Poisson-distribution,mu must be positive.

A positivenumeric vector of standard deviations for thestate-dependent distribution in the different states of lengthnstates.

Not relevant in case of a state-dependent Poisson distribution.

A positivenumeric vector of degrees of freedom for thestate-dependent distribution in the different states of lengthnstates.

Only relevant in case of a state-dependent t-distribution.

Acharacter, the stock's symbol.

It must match the identifier onhttps://finance.yahoo.com/.

Acharacter in the format"YYYY-MM-DD", setting the lowerdata bound.

Must not be earlier than"1902-01-01" (default).

Acharacter in the format"YYYY-MM-DD", setting the upperdata bound.

Default is the current dateSys.date().

Set toTRUE to fill missing dates (e.g., days at which the stockmarket is closed) withNA's.

By default,fill_dates = FALSE.

Acharacter of requested data columns, see the details.

By default, all columns are returned.

An object of classfHMM_controls.It can be created withset_controls.

EitherNULL (default) or acharacter vector of color names orhexadecimal RGB triplets.

The dates in the empirical case.

The time points in the simulated case.

The states in the simulated case.

The data for modeling.

The data before transformation.

The fine-scale chunk sizes.

ThefHMM_controls object.

ThefHMM_parameters object in the simulated case.

An object of classfHMM_data.

Currently not used.

An object of classfHMM_data.

Alist of two elements.

• The first element is named"dates" and contains acharactervector in format"YYYY-MM-DD".

• The second element is named"labels" and is acharactervector of the same length as"dates".

An object of classfHMM_events.

Currently not used.

An object of classfHMM_data.

Anumeric vector of unconstrained model estimates.

The output ofnlm for the selected optimization run.

Adiff.time object, the total estimation time.

Anumeric, the model log-likelihood.

Anumeric vector, the model log-likelihoods in all optimization runs.

Anumeric vector, the gradient at the optimum.

Anumeric vector, the inverse Fisher information for each parameter.

Anumeric vector, the decoded time series.

An object of classfHMM_model.

Currently not used.

Anumeric between 0 and 1, the confidence level.

The number of decimal places.

Passed on toAIC.

The number of time points to predict ahead.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

Alogical, set toTRUE for an hierarchical HMM.

Ifhierarchy = TRUE, some of the other controls must be specified forthe coarse-scale and the fine-scale layer.

By default,hierarchy = FALSE.

Aninteger, the number of states of the underlying Markov chain.

Ifhierarchy = TRUE,states must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,states = 2 ifhierarchy = FALSE andstates = c(2, 2) ifhierarchy = TRUE.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• meanmu,

• standard deviationsigma (not for the Poisson distribution),

• degrees of freedomdf (only for the t-distribution),

can be fixed via, e.g.,"t(df = 1)" or"gamma(mu = 0, sigma = 1)".To fix different values of a parameter for different states, separate by"|", e.g."poisson(mu = 1|2|3)".

Ifhierarchy = TRUE,sdds must be avector of length 2.The first entry corresponds to the coarse-scale layer, while the second entrycorresponds to the fine-scale layer.

By default,sdds = "normal" ifhierarchy = FALSE andsdds = c("normal", "normal") ifhierarchy = TRUE.

A transition probabilitymatrix.

It should have dimensionstates[1].

Gamma_star is alist of fine-scale transition probabilitymatrices. Thelist must be of lengthstates[1].Each transition probability matrix must be of dimensionstates[2].

Anumeric vector of expected values for the state-dependentdistribution in the different states.

For the gamma- or Poisson-distribution,mu must be positive.

It should have lengthstates[1].

mu_star is alist ofvectors with fine-scaleexpectations. Thelist must be of lengthstates[1].Eachvector must be of lengthstates[2].

A positivenumeric vector of standard deviations for thestate-dependent distribution in the different states.

It should have lengthstates[1].

sigma_star is alist ofvectors with fine-scalestandard deviations. Thelist must be of lengthstates[1].Each vector must be of lengthstates[2].

A positivenumeric vector of degrees of freedom for thestate-dependent distribution in the different states.

It should have lengthstates[1].

Only relevant in case of a state-dependent t-distribution.

df_star is alist ofvectors with fine-scaledegrees of freedom. Thelist must be of lengthstates[1].Each vector must be of lengthstates[2].Only relevant in case of a fine-scale state-dependent t-distribution.

A positivenumeric vector of length two, containing scales for sampledexpectations and standard deviations.

The first entry is the scale formu andsigma, the second entry is the scale formu_star andsigma_star (if any).

Sets a seed for the sampling of parameters.

EitherTRUE to check the defined controls orFALSE to not checkthem (which saves computation time), else.

An object of classfHMM_parameters.

Currently not used.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• meanmu,

• standard deviationsigma (not for the Poisson distribution),

• degrees of freedomdf (only for the t-distribution),

can be fixed via, e.g.,"t(df = 1)" or"gamma(mu = 0, sigma = 1)".To fix different values of a parameter for different states, separate by"|", e.g."poisson(mu = 1|2|3)".

Ifhierarchy = TRUE,sdds must be avector of length 2.The first entry corresponds to the coarse-scale layer, while the second entrycorresponds to the fine-scale layer.

By default,sdds = "normal" ifhierarchy = FALSE andsdds = c("normal", "normal") ifhierarchy = TRUE.

Aninteger, the number of states of the underlying Markov chain.

Ifhierarchy = TRUE,states must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,states = 2 ifhierarchy = FALSE andstates = c(2, 2) ifhierarchy = TRUE.

Currently not used.

[character(1)]
The date in format"YYYY-MM-DD".

An object of classfHMM_data.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

Alist of controls specifying the model fitting.

Thelist can contain the following elements, which are describedin more detail below:

• runs, defines the number of numerical optimization runs,

• origin, defines initialization at the true parameters,

• accept, defines the set of accepted optimization runs,

• gradtol, defines the gradient tolerance,

• iterlim, defines the iteration limit,

• print.level, defines the level of printing,

• steptol, defines the minimum allowable relative step length.

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values, see below.

Specifications infit override individual specifications.

Aninteger, setting the number of randomly initializedoptimization runs of the model likelihood from which the best one is selectedas the final model.

By default,runs = 10.

Only relevant for simulated data, i.e., if thedata control isNA.

In this case, alogical. Iforigin = TRUE the optimization isinitialized at the true parameter values.This setsrun = 1 andaccept = 1:5.

By default,origin = FALSE.

Aninteger (vector), specifying which optimization runs areaccepted based on the output code ofnlm.

By default,accept = 1:3.

A positivenumeric value, specifying the gradient tolerance, passed ontonlm.

By default,gradtol = 0.01.

A positiveinteger value, specifying the iteration limit, passed ontonlm.

By default,iterlim = 100.

One of0,1, and2 to control the verbosity of thenumerical likelihood optimization, passed on tonlm.

By default,print.level = 0.

A positivenumeric value, specifying the step tolerance, passed ontonlm.

By default,gradtol = 0.01.

Set the number of clusters for parallel optimization runs to reduceoptimization time.By default,ncluster = 1 (no clustering).

Set a seed for the generation of initial values.No seed by default.

Set toTRUE to print progress messages.

Optionally defines an initial estimate for the numerical likelihoodoptimization. Good initial estimates can improve the optimization process.Can be:

• NULL (the default), in this case

  • applies a heuristic to calculate a good initial estimate

  • or uses the true parameter values (if available anddata$controls$origin isTRUE)

• or an object of classparUncon (i.e., anumeric ofunconstrained model parameters), for example the estimate of apreviously fitted model (i.e. the elementmodel$estimate).

An object of classfHMM_data.

Set the number of clusters for parallel optimization runs to reduceoptimization time.By default,ncluster = 1 (no clustering).

Set a seed for the generation of initial values.No seed by default.

Set toTRUE to print progress messages.

Optionally defines an initial estimate for the numerical likelihoodoptimization. Good initial estimates can improve the optimization process.Can be:

• NULL (the default), in this case

  • applies a heuristic to calculate a good initial estimate

  • or uses the true parameter values (if available anddata$controls$origin isTRUE)

• or an object of classparUncon (i.e., anumeric ofunconstrained model parameters), for example the estimate of apreviously fitted model (i.e. the elementmodel$estimate).

[list()]
Alist.

An object of classparUncon, which is anumericvectorwith identified and unconstrained model parameters in the following order:

1. non-diagonal transition probabilitiesgammasUncon

2. expectationsmuUncon

3. standard deviationssigmaUncon (if any)

4. degrees of freedomdfUncon (if any)

5. fine-scale parameters for each coarse-scale state, in the same order (if any)

Anumericvector of time-series data.

In the hierarchical case (hierarchy = TRUE), amatrix withcoarse-scale data in the first column and corresponding fine-scale data inthe rows.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

Alogical, set toTRUE for an hierarchical HMM.

Ifhierarchy = TRUE, some of the other controls must be specified forthe coarse-scale and the fine-scale layer.

By default,hierarchy = FALSE.

Aninteger, the number of states of the underlying Markov chain.

Ifhierarchy = TRUE,states must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,states = 2 ifhierarchy = FALSE andstates = c(2, 2) ifhierarchy = TRUE.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• meanmu,

• standard deviationsigma (not for the Poisson distribution),

• degrees of freedomdf (only for the t-distribution),

can be fixed via, e.g.,"t(df = 1)" or"gamma(mu = 0, sigma = 1)".To fix different values of a parameter for different states, separate by"|", e.g."poisson(mu = 1|2|3)".

Ifhierarchy = TRUE,sdds must be avector of length 2.The first entry corresponds to the coarse-scale layer, while the second entrycorresponds to the fine-scale layer.

By default,sdds = "normal" ifhierarchy = FALSE andsdds = c("normal", "normal") ifhierarchy = TRUE.

EitherTRUE to return the negative log-likelihood value (useful foroptimization) orFALSE (default), else.

EitherTRUE to check the defined controls orFALSE to not checkthem (which saves computation time), else.

An object of classparUncon.

The matrix of the simulated or empirical data used for estimation.

An object of classfHMM_controls.

An object of classparUncon.

The vector of the simulated or empirical data used for estimation.

An object of classfHMM_controls.

An object of classfHMM_controls.

The expected output length. IfNULL (default), this is not checked.

An object of classfHMM_parameters, which is alistof model parameters.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

EitherTRUE to label the parameters orFALSE, if not (this cansave computation time).

An object of classparUncon, which is anumericvectorwith identified and unconstrained model parameters in the following order:

1. non-diagonal transition probabilitiesgammasUncon

2. expectationsmuUncon

3. standard deviationssigmaUncon (if any)

4. degrees of freedomdfUncon (if any)

5. fine-scale parameters for each coarse-scale state, in the same order (if any)

EitherTRUE orFALSE, determining whether to apply thefollowing small corrections to boundary parameters to improve numericalperformance when calculating and optimizing the likelihood function:

• transition probabilities equal to 0 or 1 are shifted towards the centerby1e-3

• standard deviations and degrees of freedom are bounded above by100

An object of classparCon, which is anumericvectorwith identified (and constrained) model parameters in the following order:

1. non-diagonal transition probabilitiesgammasCon

2. expectationsmuCon

3. standard deviationssigmaCon (if any)

4. degrees of freedomdfCon (if any)

5. fine-scale parameters for each coarse-scale state, in the same order (if any)

A vector of (un-) constrained expected values.

EitherTRUE orFALSE, determining whether to apply the linkfunction.

Acharacter prefix for labeling the parameters.

A vector of (un-) constrained standard deviations.

A vector of (un-) constrained degrees of freedom.

A vector of (un-) constrained non-diagonal transition probabilities.

Aninteger, the dimension of the transition probability matrix.

An object of classfHMM_data.

An object of classfHMM_events.

Optionally acharacter for a custom title.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the lower date bound for plotting.By default,from = NULL, i.e. no lower bound.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the upper date bound for plotting.By default,to = NULL, i.e. no upper bound.

Currently not used.

An object of classfHMM_model.

A character (vector), specifying the type of plot and can be one (or more) of

• "ll" for a visualization of the likelihood values in thedifferent optimization runs,

• "sdds" for a visualization of the estimated state-dependentdistributions,

• "pr" for a visualization of the model's (pseudo-) residuals,

• "ts" for a visualization of the financial time series.

An object of classfHMM_events.

EitherNULL (default) or acharacter vector of color names orhexadecimal RGB triplets.

Alogical, set toTRUE (default) to plot the differences fromthe best log-likelihood value. Set toFALSE to plot the absolutevalues.

Optionally acharacter for a custom title.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the lower date bound for plotting.By default,from = NULL, i.e. no lower bound.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the upper date bound for plotting.By default,to = NULL, i.e. no upper bound.

Currently not used.

Anumeric vector of log-likelihood values.

Alogical, set toTRUE (default) to plot the differences fromthe best log-likelihood value. Set toFALSE to plot the absolutevalues.

An object of classfHMM_residuals.

The elementcontrols$hierarchy.

An object of classfHMM_parameters with estimated parameters.

EitherNULL or an object of classfHMM_parameters with trueparameters.

An object of classfHMM_controls.

EitherNULL (default) or acharacter vector of color names orhexadecimal RGB triplets.

An object of classfHMM_data.

EitherNULL or an object of classfHMM_decoding.

EitherNULL (default) or acharacter vector of color names orhexadecimal RGB triplets.

An object of classfHMM_events.

Optionally acharacter for a custom title.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the lower date bound for plotting.By default,from = NULL, i.e. no lower bound.

Optionally acharacter, a date in format"YYYY-MM-DD",setting the upper date bound for plotting.By default,to = NULL, i.e. no upper bound.

An object of classfHMM_controls.

An object of classfHMM_parameters, used as simulation parameters.By default,true_parameters = NULL, i.e., sampled true parameters.

Set a seed for the data simulation.No seed per default.

An object of classfHMM_controls.

An object of classfHMM_model.

Either

• "mean", in which case the states are ordered according to the meansof the state-dependent distributions,

• or a vector (or a matrix) which determines the new ordering:

  • Ifx$data$controls$hierarchy = FALSE,state_order mustbe a vector of lengthx$data$controls$states with integervalues from1 tox$data$controls$states. If the oldstate numberx should be the new state numbery, putthe valuex at the positiony ofstate_order.E.g. for a 2-state HMM, specifyingstate_order = c(2, 1) swapsthe states.

  • Ifx$data$controls$hierarchy = TRUE,state_order mustbe a matrix of dimensionx$data$controls$states[1] xx$data$controls$states[2] + 1. The first column orders thecoarse-scale states with the logic as described above. For each row,the elements from second to last position order the fine-scale statesof the coarse-scale state specified by the first element. E.g. for anHHMM with 2 coarse-scale and 2 fine-scale states, specifyingstate_order = matrix(c(2, 1, 2, 1, 1, 2), 2, 3) swaps thecoarse-scale states and the fine-scale states connected tocoarse-scale state 2.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

Alogical, set toTRUE for an hierarchical HMM.

Ifhierarchy = TRUE, some of the other controls must be specified forthe coarse-scale and the fine-scale layer.

By default,hierarchy = FALSE.

Aninteger, the number of states of the underlying Markov chain.

Ifhierarchy = TRUE,states must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,states = 2 ifhierarchy = FALSE andstates = c(2, 2) ifhierarchy = TRUE.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• meanmu,

• standard deviationsigma (not for the Poisson distribution),

• degrees of freedomdf (only for the t-distribution),

can be fixed via, e.g.,"t(df = 1)" or"gamma(mu = 0, sigma = 1)".To fix different values of a parameter for different states, separate by"|", e.g."poisson(mu = 1|2|3)".

Ifhierarchy = TRUE,sdds must be avector of length 2.The first entry corresponds to the coarse-scale layer, while the second entrycorresponds to the fine-scale layer.

By default,sdds = "normal" ifhierarchy = FALSE andsdds = c("normal", "normal") ifhierarchy = TRUE.

Anumeric, specifying the length of the time horizon.

Ifhierarchy = TRUE,horizon must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,horizon = 100 ifhierarchy = FALSE andhorizon = c(100, 30) ifhierarchy = TRUE.

Ifdata is specified (i.e., notNA), the first entry ofhorizon is ignored and the (coarse-scale) time horizon is defined byavailable data.

Only relevant ifhierarchy = TRUE.

In this case, acharacter which specifies a flexible, periodicfine-scale time horizon and can be one of

• "w" for a week,

• "m" for a month,

• "q" for a quarter,

• "y" for a year.

By default,period = NA. Ifperiod is notNA, itoverruleshorizon[2].

EitherNA, in which case data is simulated (the default), or alist of controls specifying the empirical data set.

Thelist can contain the following elements, which are describedin more detail below:

• file, defines the data set,

• date_column, defines the date column,

• data_column, defines the data column,

• from, defines a lower date limit,

• to, defines an upper date limit,

• logreturns, defines a data transformation to log-returns,

• merge, defines the merging for coarse-scale observations.

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values, see below.

Specifications indata override individual specifications.

Adata.frame with data and dates for modeling.

Ifhierarchy = TRUE,file can be alist oflength 2. The first entry is adata.frame and provides the data forthe coarse-scale layer, while the second entry corresponds to the fine-scalelayer. Iffile is a singledata.frame, then the samedata.frame is used for both layers.

Alternatively, it can be acharacter (of length two), the path to a.csv-file with financial data.

Acharacter, the name of the column infile with dates.

Ifhierarchy = TRUE andfile is alist of twodata.frames,data_column must be avector oflength 2. The first entry corresponds to the coarse-scale layer, while thesecond entry corresponds to the fine-scale layer.

By default,date_column = "Date".

Acharacter, the name of the column infile with observations.

Ifhierarchy = TRUE,data_column must be avector oflength 2. The first entry corresponds to the coarse-scale layer, while thesecond entry corresponds to the fine-scale layer.

By default,data_column = "Close" ifhierarchy = FALSE anddata_column = c("Close", "Close") ifhierarchy = TRUE.

Acharacter of the format"YYYY-MM-DD", setting a lowerdate limit. No lower limit iffrom = NA (default).

Acharacter of the format"YYYY-MM-DD", setting an upperdate limit. No lower limit ifto = NA (default).

Alogical, ifTRUE the data is transformed to log-returns.

Ifhierarchy = TRUE,logreturns must be avector oflength 2. The first entry corresponds to the coarse-scale layer, while thesecond entry corresponds to the fine-scale layer.

By default,logreturns = FALSE ifhierarchy = FALSE andlogreturns = c(FALSE, FALSE) ifhierarchy = TRUE.

Only relevant ifhierarchy = TRUE.

In this case, afunctionwhich merges an input numeric vector of fine-scale datax into onecoarse-scale observation. For example,

• merge = function(x) mean(x) (default) defines the mean of thefine-scale data as the coarse-scale observation,

• merge = function(x) mean(abs(x)) for the mean of theabsolute values,

• merge = function(x) sum(abs(x)) for the sum of theabsolute values,

• merge = function(x) (tail(x, 1) - head(x, 1)) / head(x, 1) forthe relative change of the first to the last fine-scale observation.

Alist of controls specifying the model fitting.

Thelist can contain the following elements, which are describedin more detail below:

• runs, defines the number of numerical optimization runs,

• origin, defines initialization at the true parameters,

• accept, defines the set of accepted optimization runs,

• gradtol, defines the gradient tolerance,

• iterlim, defines the iteration limit,

• print.level, defines the level of printing,

• steptol, defines the minimum allowable relative step length.

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values, see below.

Specifications infit override individual specifications.

Aninteger, setting the number of randomly initializedoptimization runs of the model likelihood from which the best one is selectedas the final model.

By default,runs = 10.

Only relevant for simulated data, i.e., if thedata control isNA.

In this case, alogical. Iforigin = TRUE the optimization isinitialized at the true parameter values.This setsrun = 1 andaccept = 1:5.

By default,origin = FALSE.

Aninteger (vector), specifying which optimization runs areaccepted based on the output code ofnlm.

By default,accept = 1:3.

A positivenumeric value, specifying the gradient tolerance, passed ontonlm.

By default,gradtol = 0.01.

A positiveinteger value, specifying the iteration limit, passed ontonlm.

By default,iterlim = 100.

One of0,1, and2 to control the verbosity of thenumerical likelihood optimization, passed on tonlm.

By default,print.level = 0.

A positivenumeric value, specifying the step tolerance, passed ontonlm.

By default,gradtol = 0.01.

An object of classfHMM_controls.

Currently not used.

Either alist or an object of classfHMM_controls.

Thelist can contain the following elements, which are describedin more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, alist of controls that define the data,

• fit, alist of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values.

Important: Specifications incontrols always override individualspecifications.

Alogical, set toTRUE for an hierarchical HMM.

Ifhierarchy = TRUE, some of the other controls must be specified forthe coarse-scale and the fine-scale layer.

By default,hierarchy = FALSE.

Aninteger, the number of states of the underlying Markov chain.

Ifhierarchy = TRUE,states must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,states = 2 ifhierarchy = FALSE andstates = c(2, 2) ifhierarchy = TRUE.

Acharacter, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• meanmu,

• standard deviationsigma (not for the Poisson distribution),

• degrees of freedomdf (only for the t-distribution),

can be fixed via, e.g.,"t(df = 1)" or"gamma(mu = 0, sigma = 1)".To fix different values of a parameter for different states, separate by"|", e.g."poisson(mu = 1|2|3)".

Ifhierarchy = TRUE,sdds must be avector of length 2.The first entry corresponds to the coarse-scale layer, while the second entrycorresponds to the fine-scale layer.

By default,sdds = "normal" ifhierarchy = FALSE andsdds = c("normal", "normal") ifhierarchy = TRUE.

Anumeric, specifying the length of the time horizon.

Ifhierarchy = TRUE,horizon must be avector of length2. The first entry corresponds to the coarse-scale layer, while the secondentry corresponds to the fine-scale layer.

By default,horizon = 100 ifhierarchy = FALSE andhorizon = c(100, 30) ifhierarchy = TRUE.

Ifdata is specified (i.e., notNA), the first entry ofhorizon is ignored and the (coarse-scale) time horizon is defined byavailable data.

Only relevant ifhierarchy = TRUE.

In this case, acharacter which specifies a flexible, periodicfine-scale time horizon and can be one of

• "w" for a week,

• "m" for a month,

• "q" for a quarter,

• "y" for a year.

By default,period = NA. Ifperiod is notNA, itoverruleshorizon[2].

An object of classfHMM_parameters, used as simulation parameters.By default,true_parameters = NULL, i.e., sampled true parameters.

Set a seed for the data simulation.No seed per default.

Anumeric vector of states of a Markov chain.

Acharacter, the name of the state-dependent distribution.

Anumeric vector of expected values.

Anumeric vector of standard deviations (if any).

Anumeric vector of degrees of freedom (if any).

Sets a seed for the observation sampling.

Aninteger, the total length of the output vector.Must be greater or equal thanlength(markov_chain).