Empirical measures of signed serial dependence in categorical time series

Abstract

The categorical time series analysis has become an area of emerging interest both in research and professional practice. In this article, we propose empirical measures of signed serial dependence, which are particularly important for identifying and fitting an appropriate model to a given categorical time series. We derive asymptotic properties of these measures and a rule for identifying significant dependence. We investigate the finite-sample performance of the proposed measures in a simulation study and show that they are sensitive to both positive and negative serial dependence even for rather short time series.

Keywords:

• categorical time series
• signed serial dependence
• Cohen's κ
• Gini index
• NDARMA models
• Markov chain

Acknowledgements

The author thanks the referee for the useful comments on an earlier draft of this article.