stan_ssm: Fitting an Additive linear State space model.
In bayesforecast: Bayesian Time Series Modeling with Stan

Description Usage Arguments Details Value Author(s) References See Also Examples

Fitting an Additive linear State space model in Stan.

stan_ssm(
  ts,
  trend = FALSE,
  damped = FALSE,
  seasonal = FALSE,
  xreg = NULL,
  period = 0,
  genT = FALSE,
  chains = 4,
  iter = 2000,
  warmup = floor(iter/2),
  adapt.delta = 0.9,
  tree.depth = 10,
  stepwise = TRUE,
  prior_sigma0 = NULL,
  prior_level = NULL,
  prior_level1 = NULL,
  prior_trend = NULL,
  prior_trend1 = NULL,
  prior_damped = NULL,
  prior_seasonal = NULL,
  prior_seasonal1 = NULL,
  prior_breg = NULL,
  prior_df = NULL,
  series.name = NULL,
  ...
)

`ts`	a numeric or ts object with the univariate time series.
`trend`	a boolean value to specify a trend local level model. By default is `FALSE`.
`damped`	a boolean value to specify a damped trend local level model. By default is `FALSE`. If `trend` option is `FALSE` then `damped` is set to `FALSE` automatically.
`seasonal`	a boolean value to specify a seasonal local level model. By default is `FALSE`.
`xreg`	Optionally, a numerical matrix of external regressors, which must have the same number of rows as ts. It should not be a data frame.
`period`	an integer specifying the periodicity of the time series by default the value frequency(ts) is used.
`genT`	a boolean value to specify for a generalized t-student SSM model.
`chains`	An integer of the number of Markov Chains chains to be run, by default 4 chains are run.
`iter`	An integer of total iterations per chain including the warm-up, by default the number of iterations are 2000.
`warmup`	A positive integer specifying number of warm-up (aka burn-in) iterations. This also specifies the number of iterations used for step-size adaptation, so warm-up samples should not be used for inference. The number of warmup should not be larger than `iter` and the default is `iter/2`.
`adapt.delta`	An optional real value between 0 and 1, the thin of the jumps in a HMC method. By default is 0.9.
`tree.depth`	An integer of the maximum depth of the trees evaluated during each iteration. By default is 10.
`stepwise`	If TRUE, will do stepwise selection (faster). Otherwise, it searches over all models. Non-stepwise selection can be very slow, especially for seasonal models.
`prior_sigma0`	The prior distribution for the scale parameter in an SSM model. By default the value is set `NULL`, then the default student(7,0,1) prior is used.
`prior_level`	The prior distribution for the level parameter in a SSM model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_level1`	The prior distribution for the initial level parameter in a SSM model. By default the value is set `NULL`, then the default student(6,0,2.5) priors are used.
`prior_trend`	The prior distribution for the trend parameter in a SSM model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_trend1`	The prior distribution for the initial trend parameter in a SSM model. By default the value is set `NULL`, then the default student(6,0,2.5) priors are used.
`prior_damped`	The prior distribution for the damped trend parameter in a SSM model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_seasonal`	The prior distribution for the seasonal parameter in a SSM model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_seasonal1`	The prior distribution for the initial seasonal parameters in a SSM model. The prior is specified for the first m seasonal parameters, where m is the periodicity of the defined time series. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_breg`	The prior distribution for the regression coefficient parameters in a ARMAX model. By default the value is set `NULL`, then the default student(7,0,1) priors are used.
`prior_df`	The prior distribution for the degree freedom parameters in a t-student innovations SSM model. By default the value is set `NULL`, then the default gamma(2,0.1) priors are used.
`series.name`	an optional string vector with the series names.
`...`	Further arguments passed to `varstan` function.

The function returns a varstan object with the fitted model.

By default the ssm() function generates a local level model (or a ets("A","N","N") or exponential smoothing model from the forecast package). If trend is set TRUE, then a local trend ssm model is defined (a equivalent ets("A","A","N") or Holt model from the forecast package). For damped trend models set damped to TRUE. If seasonal is set to TRUE a seasonal local level model is defined (a equivalent ets("A","N","A") model from the forecast package). For a Holt-Winters method (ets("A","A","A")) set Trend and seasonal to TRUE.

When genT option is TRUE a t-student innovations ssm model (see Ardia (2010)) is generated see Fonseca, et. al (2019) for more details.

The default priors used in a ssm( ) model are:

level ~ normal(0,0.5)
Trend ~ normal(0,0.5)
damped~ normal(0,0.5)
Seasonal ~ normal(0,0.5)
sigma0 ~ t-student(0,1,7)
level1 ~ normal(0,1)
trend1 ~ normal(0,1)
seasonal1 ~ normal(0,1)
dfv ~ gamma(2,0.1)
breg ~ t-student(0,2.5,6)

For changing the default prior use the function set_prior().

A varstan object with the fitted SSM model.

Asael Alonzo Matamoros.

Fonseca, T. and Cequeira, V. and Migon, H. and Torres, C. (2019). The effects of degrees of freedom estimation in the Asymmetric GARCH model with Student-t Innovations. arXiv doi: arXiv: 1910.01398.

Sarima auto.arima set_prior garch

 # Declaring a local level model for the ipc data.
 sf1 = stan_ssm(ipc,iter = 500,chains = 1)

 # Declaring a Holt model for the ipc data.
 sf2 = stan_ssm(ipc,trend = TRUE,damped = TRUE,iter = 500,chains = 1)