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I'd like to fit a non stationary time series using a SARIMA + GARCH model. I have not found any package that allow me to fit this model. I'm using rugarch:

model=ugarchspec(
  variance.model = list(model = "sGARCH", garchOrder = c(1, 1)),
  mean.model = list(armaOrder = c(2, 2), include.mean = T),
  distribution.model = "sstd")
modelfit=ugarchfit(spec=model,data=y)

but it allow me only to fit an ARMA + GARCH model.
Can you help me?

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  • $\begingroup$ I'd settle for an ARIMA + GARCH $\endgroup$
    – Manuel
    Mar 27, 2015 at 10:26

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You find R code for seasonal ARIMA models again in the book mentioned (this chapter). Do you really need the GARCH errors?

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  • $\begingroup$ Yes, I have to try this model but I never use GARCH in R. I know how to do a SARIMA model in R, I used: mod <- arima(y, order= c(p,d,q),seasonal = list (order = c (P,D,Q), period = m)), but I don't know how to create with an only function a SARIMA + GARCH model. Another way is to create before a SARIMA model and then fit residuals with a GARCH model, right? With this approach how can I do to use the GARCH errors in the SARIMA? thank you for your help! $\endgroup$
    – Manuel
    Mar 27, 2015 at 14:30
  • $\begingroup$ Yes, that's one way to go: first fit an Arima model and then fit a GARCH model to the errors. The prediction of the Arima model will not depend on the GARCH error - confidence intervals however will. $\endgroup$
    – Richi Wa
    Apr 27, 2015 at 6:50
  • $\begingroup$ Richard, efficient estimators of the conditional mean model (the ARIMA part) depend on the conditional variance model (the GARCH part). Using efficient estimators would mean that the forecasts of ARIMA will be different depending on whether GARCH is included or not. While you can take estimators that do not have this property, they will generally be statistically inferior (less efficient). But they will be computationally simpler, of course. @Manuel $\endgroup$
    – Richard Hardy
    Apr 3, 2017 at 13:19
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While SARIMA-GARCH is not currently (October 2016) implemented in R as far as I am aware, you can deal with seasonality by including some dummy variables or Fourier terms in the conditional mean model. 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.

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  • $\begingroup$ Thank you for your answer @Richard Hardy, but what should I write inside the argument "external.regressors" if my Model for example SARIMA (1, 1, 3)(2, 1, 1)7 and since my data is huge how can i identify $\endgroup$
    – Karim Ch
    Sep 8, 2021 at 22:10
  • $\begingroup$ @KarimCh, dummy variables or Fourier terms. You can find descriptions of how to use these for modelling seasonality in time series textbooks and Rob J. Hyndman's blog (search for Fourier). $\endgroup$
    – Richard Hardy
    Sep 9, 2021 at 5:38

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