Forecasting of Categorical Time Series Using a Regression Model

This paper deals with time series of categorical or ordinal variables, which are combined with time varying covariates. The conditional expectations (probabilities) are modelled as a regression model in a GLM-type manner, its parameters are estimated using a (partial) likelihood-approach. Special attention is given to the multivariate and the cumulative logistic regression model, with a regression term defined by a recursive scheme. The main concern is directed at forecasts for such time series. Using an approximation formula for conditional expectations l-step predictors are developed. Bias and mean square errors are estimated by using expansion formulas and by employing Box-Jenkins as well as nonparametric methods. The procedures proposed are numerically applied to a data set of yearly forest health inventories.