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. Biswas and Guha (2009) used mutual information as a measure of association and introduced the concept of auto-mutual information in this context. In this present paper we generalise to auto-power divergence measures for this purpose and study some special cases. Theoretical properties and simulation results are given along with an illustrative real data example.