# Forecasting AR-ARCH/GARCH models

I have a simple theoretical question as I am a beginner in time series analysis.

The idea of modeling an AR-ARCH or GARCH is to model the mean and the variance. After modeling, I want to forecast the mean.

I know that I will need to forecast the variance too.

But when I write the formula, for example, for the one-step-ahead forecast of the conditional mean, the one-step-ahead forecast of the conditional variance, $\hat\sigma_{t+1}^2$, doesn´t show up.

That's where my doubts come from. How can I see the benefits in modeling and forecasting the variance when my goal is modeling and forecasting the mean?

And second: For what purpose would I use my estimated variance and make your prediction?
Would it be just to build a confidence interval for the expected mean? In this case, obviously, the confidence interval would not be a straight line because the conditional variance is non-constant.

• I fixed some grammatical mistakes, but I could not figure out what you meant here: and make your prediction? Anyway, I hope I addressed the correct questions in my answer. Commented Oct 3, 2015 at 21:07