Some Forecast Methods in Regression Models for Categorical Time Series

We are dealing with the prediction of forthcoming outcomes of a
categorical time series. We will assume that the evolution of the
time series is driven by a covariate process and by former outcomes
and that the covariate process itself obeys an autoregressive law.
Two forecasting methods are presented. The first is based on an
integral formula for the probabilities of forthcoming events and by
a Monte Carlo evaluation of this integral. The second method makes
use of an approximation formula for conditional expectations. The
procedures proposed are illustrated by an application to data on
forest damages.