Adjusting Forecast Intervals in Arch-M Models

In this paper, we extend predictor expressions from an ARMA model with GARCH(1,1) innovations that allow for the conditional variance to be a regressor variable. We also obtain all the theoretical moments of the multi-step prediction error distribution from this model. The forecast error has a distribution that depends nontrivially on the information set and, therefore, the classical forecast intervals do not work well. To improve those forecast intervals, we suggest adjusting the quantile of the conditional distribution for the s-step-ahead forecast error by means of the Cornish-Fisher asymptotic expansion