# SARIMA+GARCH model

The model ARIMA+GARCH writing as this form with the rugarch package in R:

spec=ugarchspec(variance.model=list(garchOrder=c(1,1)),
mean.model=list(armaOrder=c(2,1)))


My Question: How to write in case if the model SARIMA+GARCH in R?

Where SARIMA model:

Model <- Arima(data,order=c(2,1,2),seasonal=list(order=c(1,0,0),12))

• So... at the end, how did you solve it? Did you use SARIMA residuals into the GARCH specification with armaOrder=c(0,0) ? – Luis Arturo Apr 3 at 0:24

If you are using the "rugarch" package in R, you can include these terms via the argument external.regressors within the argument mean.model in the ugarchspec function.

From CRAN:

external.regressors A matrix object containing the external regressors to include in the mean equation with as many rows as will be included in the data (which is passed in the fit function).

For further reference: https://otexts.com/fpp2/seasonal-arima.html

• Thank you very much. – Remal Aug 29 '19 at 4:10
• I don' think that works because SARIMA does not contain external regressors. SARIMA is actually an ARIMA with coefficient restrictions. I am not aware of an R package that allows estimating SARIMA+GARCH models. – Richard Hardy Sep 13 '19 at 9:19