How SARIMA and GARCH Could Be Combined for Forecasting

Summary

The document raises a conceptual question about combining seasonal ARIMA and GARCH models for time-series forecasting. It distinguishes the familiar SARIMA prediction of future series values from a GARCH forecast, which the author understands as producing forecasts of conditional variance rather than the series level. The central issue is how a combined model should generate a forecast and what it means to describe a prediction as SARIMA–GARCH.

No answer or worked method is included, so the document does not specify a fitting sequence, equations, or a concrete forecasting procedure. It is useful as a statement of the modeling distinction that needs clarification: a mean or level model and a conditional-volatility model address different parts of a time series. The post alone does not establish how to combine them, how seasonal effects enter volatility, or how to evaluate forecast performance.

Key ideas

• The question distinguishes forecasts of series values from forecasts of conditional variance.
• SARIMA is presented as a method for predicting future values of a seasonal time series.
• GARCH forecasting is understood by the author as forecasting variance rather than the level.
• The document asks what a combined SARIMA–GARCH prediction means but provides no solution.

Tags

# Combining SARIMA and GARCH model for prediction in python


# Combining SARIMA and GARCH model for prediction in python












I need to understand the concept of combining (S)ARIMA and (G)ARCH model for the predicting time-series data.

I understand that after fitting the arima model `model.predict(n_periods=n)` gives the prediction for next n series.

I think `model.forecast(horizon=n)` for garch gives the variance forecast and not the "real forecast" ?

How do you predict combining both GARCH and SARIMA model? what does it mean that one has used SARIMA-GARCH for the prediction?

I understand, that this should be the very basic concept but I am struggling to grasp the concept. Thank you

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