Modeling Seasonal Mean Structure with GARCH Errors in R

Summary

The document asks how to fit a seasonal ARIMA model with GARCH errors in R. It notes that the rugarch specification shown supports an ARMA mean with a GARCH variance model, but does not directly provide the requested SARIMA-GARCH combination. The suggested workaround is to represent seasonality in the conditional mean using dummy variables or Fourier terms, then pass those regressors through rugarch's external.regressors setting.

The exchange offers implementation guidance rather than a fitted example, simulation, or empirical comparison. One response also points readers toward a separate source for seasonal ARIMA code and asks whether GARCH errors are necessary. The discussion is limited to the package capabilities as understood in 2016; it does not establish that the workaround is equivalent to a full seasonal ARIMA error structure or address model selection, estimation quality, or forecasting performance. Researchers should check current package functionality and validate the chosen seasonal specification against their data.

Key ideas

• The described rugarch setup fits an ARMA-GARCH model but does not directly specify seasonal ARIMA terms.
• Seasonality can be represented in the conditional mean with dummy variables or Fourier terms.
• The suggested way to supply those seasonal terms is through external regressors in the mean model.
• The discussion does not compare the workaround with a full SARIMA-GARCH model or report empirical results.

Tags

# How to fit a SARIMA + GARCH in R?


# How to fit a SARIMA + GARCH in R?












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?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/17132

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

## Answer by Richard Hardy (score 2)

https://quant.stackexchange.com/a/30466

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.