This project is concerned with establishing some of the econometric theory for predicting from models involving time dependent conditional variances. Specifically, the intention is to examine the form of the optimal predictor of the conditional mean and the conditional variance equations; their mean squared error (MSE) and their associated multi-step prediction density. Initial work that has been undertaken has given rise to analytic expressions for all the moments of the conditional mean prediction density from a univariate autocorrelated process with GARCH (1,1) innovations. The project will extend these results for more general processes and will attempt to derive some fairly general results for the prediction of future conditional variances. It is anticipated that there will be many applications of these results in asset pricing models and option pricing models, where prediction of future volatility is likely to be important an important component of the asset price. Applications will also be made to the relationship between stock market indices and the real business cycle.
