Regression Models for Non‐stationary Categorical Time Series

Abstract. Categorical time series often exhibit non‐stationary behaviour, due to the influence of exogenous variables. A parsimonious and flexible class of models is proposed for the statistical analysis of such data. These models are extensions of regression models for stochastically independent observations. Statistical inference can be based on asymptotic properties of the maximum likelihood estimator and of test statistics for linear hypotheses. Weak conditions assuring these properties are stated. Some tests which are of special interest in the time series situation are treated in more detail, for example tests of stationarity or independence of parallel time series.