For stationary time series of nominal categorical data or ordinal categorical data (with arbitrary ordered numberings of the categories), autocorrelation does not make much sense. One can alternatively think of
using some entropic measures, of which a measure introduced by Havrda and Charvat (1967) could be particularly useful. We discuss some theoretical properties of measures from this class in the context of categorical
time series and look at specific examples. Theoretical properties and simulation results are given along with an illustrative real data example.