What GARCH Models Forecast: Returns and Conditional Volatility

Summary

The document raises questions about modeling oil spot price log returns with an ARMA mean equation and conditional volatility models such as GARCH, APARCH, and EGARCH. It asks whether a forecasting function returns expected returns, volatility, or both, and whether volatility forecasts are useful when the goal is predicting price direction rather than valuing options.

It also considers why alternative volatility specifications matter if the return forecast from the chosen mean model becomes constant or zero at longer horizons. The text describes the model setup and the researcher's observations from ACF and PACF plots, but supplies no answers, forecast comparisons, or performance evidence. Its value is as a framing of the distinction between forecasting the conditional mean and forecasting conditional variance; resolving the questions requires model-specific output details and empirical validation.

Key ideas

• An ARMA equation models the conditional mean of returns, while a GARCH-family equation models conditional variance.
• A volatility forecast describes uncertainty and does not by itself predict whether prices will rise or fall.
• Different volatility specifications can matter for risk estimates even when mean forecasts converge to a constant.
• The document poses these issues but does not provide empirical answers or compare model performance.

Tags

# GARCH modelling and forecasting


# GARCH modelling and forecasting












I have a few questions regarding GARCH modelling and forecasting and it would be great if someone could help me. I am modelling the log return of oil spot prices using various GARCH models: GARCH, APARCH, EGARCH... and I am trying to forecast the prices. I found using ACF and PACF plots that the best model for the series is ARMA(0,1) and then the best model for the error term follows GARCH(1,1) or APARCH(1,1) etc

Here are my questions:

1) garch1<-garchFit(~arma(0,1)+garch(1,1),data=brentlog,trace=FALSE,include.mean=TRUE) predict(garch1,n.ahead=25) I have a doubt whether I am forecasting the volatility of the prices or the actual values of return?

2) Since I am not looking at options, there is no point forecasting the volatility right? because it won't tell me whether prices will go up or down

3) Since I have an ARMA(0,1) for my model, my forecasts will always be constant and if I don't include a mean in the model then the forecasts are the same using egarch, garch, aparch or any model: it is 0. So is there a point of using those different models in this case?

thanks a lot!

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.