Auto-association measures for stationary time series of categorical data

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 (J Stat Plan Infer 139:3076–3087, <CitationRef CitationID="CR5">2009a</CitationRef>) used mutual information as a measure of association and introduced the concept of auto-mutual information in this context. In this present paper, we introduce general auto-association measures for this purpose and study several special cases. Theoretical properties and simulation results are given along with two illustrative real data examples. Copyright Sociedad de Estadística e Investigación Operativa 2014