Choosing GARCH for Returns Versus Volatility Forecasting

Summary

The document asks which GARCH-family model is best for forecasting daily stock returns. The replies clarify that ARCH and GARCH variants are primarily used to model conditional volatility, including its time variation and clustering, rather than to predict the return itself. This distinction is central when choosing a model for a forecasting task.

For return modeling, one reply suggests an ARIMA model on log prices, with differencing intended to address nonstationarity, and offers ARIMA(1,1,1) as a heuristic starting point. It recommends checking higher-order candidates using information criteria such as AIC or BIC. The discussion is brief and does not compare models on Apple data or provide forecast evaluation. Its ARIMA guidance is also underspecified: differencing log prices produces returns, and the appropriate model order should be established for the specific series and forecasting objective.

Key ideas

• GARCH-family models primarily forecast conditional volatility rather than the return itself.
• Return forecasts require a model for the conditional mean, which may be specified separately from volatility.
• The reply offers ARIMA as a possible return-modeling approach and ARIMA(1,1,1) as a heuristic starting point.
• Candidate model orders should be evaluated with selection criteria, and no empirical comparison is provided.

Tags

# What is the best GARCH model for forecasting daily stock return and why?


# What is the best GARCH model for forecasting daily stock return and why?












If I want to forecast daily stock return let say Apple what would be the best GARCH model and why? (ARCH, GARCH-M, IGARCH, EGARCH, TARCH etc)

## Answer by JPN (score 2)

https://quant.stackexchange.com/a/44966

GARCH models are usually used to predict volatility, not returns.

## Answer by alexbougias (score 0)

https://quant.stackexchange.com/a/45013

You cannot use GARCH. The models you mentioned are used for modelling the conditional volatility, which is time-varying and displays clustering,as Mandelbrot mentioned.

A common model is an ARIMA(p,q,1), where p the order of the AR component and q the MA component. Simply, it is an ARMA(p,q) on the first differences of the log prices. This is due to the non stationarity of the log prices that drive ACF and PACF being significant for a long period of time (known as long memory process). Hence the first differences make the process stationary "cutting" the PACF and ACF shortly. As a heuristic, you can use an ARIMA(1,1,1) model, but technically speaking someone has to check higher order models as well. Model selection criteria, such as AIC or BIC have to be used.

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