Prediction in Dynamic Models with Time Dependent Conditional Variances

Abstract

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptomatotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results.