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,
prior_mu0 = NULL,
prior_sigma0 = NULL,
prior_ar = NULL,
prior_ma = NULL,
prior_sar = NULL,
prior_sma = NULL,
prior_breg = NULL,
series.name = NULL,
...
)A varstan object with the fitted SARIMA model.
a numeric or ts object with the univariate time series.
a three length vector with the specification of the non-seasonal
part of the ARIMA model. The three components c(p, d, q) are the AR,
the number of differences, and the MA orders respectively.
a three length vector with the specification of the seasonal
part of the ARIMA model. The three components c(P, D, Q) are the seasonal AR,
the degree of seasonal differences, and the seasonal MA orders respectively.
Optionally, a numerical matrix of external regressors, which must have the same number of rows as ts. It should not be a data frame.
an integer specifying the periodicity of the time series. By
default, period = frequency(ts).
an integer of the number of Markov Chains chains to be run. By
default, chains = 4.
an integer of total iterations per chain including the warm-up. By
default, iter = 2000.
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 iteration should not be larger than iter.By default,
warmup = iter/2.
an optional real value between 0 and 1, the thin of the jumps in a HMC method. By default, is 0.9.
an integer of the maximum depth of the trees evaluated during each iteration. By default, is 10.
The prior distribution for the location parameter in an
ARIMA model. By default, sets student(7,0,1) prior.
The prior distribution for the scale parameter in an
ARIMA model. By default, declares a student(7,0,1) prior.
The prior distribution for the auto-regressive parameters in an
ARIMA model. By default, sets a normal(0,0.5) priors.
The prior distribution for the moving average parameters in
an ARIMA model. By default, sets a normal(0,0.5) priors.
The prior distribution for the seasonal auto-regressive
parameters in a SARIMA model. By default, uses normal(0,0.5) priors.
The prior distribution for the seasonal moving average
parameters in a SARIMA model. By default, uses normal(0,0.5) priors.
The prior distribution for the regression coefficient
parameters in a ARIMAX model. By default, uses student(7,0,1) priors.
an optional string vector with the series names.
Further arguments passed to varstan function.
Asael Alonzo Matamoros
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 model 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)
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, and set_prior.
# \donttest{
# 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)
# }
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