stan_sarima: Fitting a Multiplicative Seasonal ARIMA model.
In bayesforecast: Bayesian Time Series Modeling with Stan

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

Fitting a SARIMA model in Stan.

stan_sarima(
  ts,
  order = c(1, 0, 0),
  seasonal = c(0, 0, 0),
  xreg = NULL,
  period = 0,
  chains = 4,
  iter = 2000,
  warmup = floor(iter/2),
  adapt.delta = 0.9,
  tree.depth = 10,
  stepwise = TRUE,
  prior_mu0 = NULL,
  prior_sigma0 = NULL,
  prior_ar = NULL,
  prior_ma = NULL,
  prior_sar = NULL,
  prior_sma = NULL,
  prior_breg = NULL,
  series.name = NULL,
  ...
)

`ts`	a numeric or ts object with the univariate time series.
`order`	A specification of the non-seasonal part of the ARIMA model: the three components (p, d, q) are the AR order, the number of differences, and the MA order.
`seasonal`	A specification of the seasonal part of the ARIMA model,same as order parameter: the three components (p, d, q) are the seasonal AR order, the degree of seasonal differences, and the seasonal MA order.
`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.
`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_mu0`	The prior distribution for the location parameter in an ARIMA model. By default the value is set `NULL`, then the default student(7,0,1) prior is used.
`prior_sigma0`	The prior distribution for the scale parameter in an ARIMA model. By default the value is set `NULL`, then the default student(7,0,1) prior is used.
`prior_ar`	The prior distribution for the auto-regressive parameters in an ARIMA model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_ma`	The prior distribution for the moving average parameters in an ARIMA model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_sar`	The prior distribution for the seasonal auto-regressive parameters in a SARIMA model. By default the value is set `NULL`, then the default normal(0,0.5) priors are used.
`prior_sma`	The prior distribution for the seasonal moving average parameters in a SARIMA model. 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 ARIMAX model. By default the value is set `NULL`, then the default student(7,0,1) 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.

If xreg option is used, the model by default will cancel the seasonal differences adjusted (D = 0). If a value d > 0 is used, all the regressor variables in xreg will be difference as well.

The default priors used in Sarima are:

ar ~ normal(0,0.5)
ma ~ normal(0,0.5)
mu0 ~ t-student(0,2.5,6)
sigma0 ~ t-student(0,1,7)
sar ~ normal(0,0.5)
sma ~ normal(0,0.5)
breg ~ t-student(0,2.5,6)

A varstan object with the fitted SARIMA model.

Asael Alonzo Matamoros

Box, G. E. P. and Jenkins, G.M. (1978). Time series analysis: Forecasting and control. San Francisco: Holden-Day. Biometrika, 60(2), 297-303. doi:10.1093/biomet/65.2.297.

Kennedy, P. (1992). Forecasting with dynamic regression models: Alan Pankratz, 1991. International Journal of Forecasting. 8(4), 647-648. url: https://EconPapers.repec.org/RePEc:eee:intfor:v:8:y:1992:i:4:p:647-648.

Hyndman, R. & Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of Statistical Software. 26(3), 1-22.doi: 10.18637/jss.v027.i03

garch set_prior

 library(astsa)
 # Declare a multiplicative seasonal ARIMA model for the birth data.
 sf1 = stan_sarima(birth,order = c(0,1,2),
                   seasonal = c(1,1,1),iter = 500,chains = 1)


 #Declare an Dynamic Harmonic Regression model for the birth data.
 sf2 = stan_sarima(birth,order = c(1,0,1),
                   xreg = fourier(birth,K = 2),iter = 500,chains = 1)