Representing Seasonal ARIMA Effects in a GARCH Model

Summary

The document asks how to combine a seasonal ARIMA mean specification with a GARCH volatility model in R. One answer suggests representing seasonal effects through the mean model’s external regressors, which requires supplying a regressor matrix aligned with the fitted observations. Another proposes fitting the seasonal ARIMA model first, then applying a GARCH specification with no additional ARMA terms to its residuals.

These are brief suggestions rather than a worked comparison or complete implementation guide. They describe different modeling routes: incorporating seasonal structure into the mean equation, or modeling volatility in residuals produced by a separate seasonal fit. The document gives no empirical results or diagnostics to establish which route is preferable. Model choice would depend on the data and on checking that the mean and volatility components are specified appropriately.

Key ideas

• Seasonal structure may be represented in the GARCH model’s mean equation using external regressors.
• An alternative is to fit seasonal ARIMA first and model its residuals with GARCH.
• The answers provide no empirical comparison of the two approaches.
• Model adequacy must be assessed on the data being analyzed.

Tags

# SARIMA+GARCH model


# 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))`

## Answer by Vitomir (score 1)

https://quant.stackexchange.com/a/47333

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

## Answer by Tendai Makoni (score 0)

https://quant.stackexchange.com/a/74558

I think you can fit SARIMA model residuals into the GARCH specification with armaOrder=c(0,0)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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