Analysis and Modeling of Categorical Time Series: Difficulties and Possible Solutions

During the last years, there has been growing interest in time series with a categorical range. Due to this type of range, standard tools of time series analysis cannot be applied, not even a plot of such categorical time series is easily possible. Therefore, this presentation aims at providing an overview of possible ways of analyzing categorical time series. Among others, types of serial dependence within categorical processes and corresponding measures are discussed, their properties are analyzed.
A possible application of such tools for analyzing categorical time series is the identification and fitting of appropriate models. One candidate is the NDARMA model, which is a discrete counterpart to the usual ARMA model and shows an ARMA-like serial dependence structure (in terms of the above measures). But also further types of models for categorical time series are surveyed.