Time series analysis of categorical data using auto-mutual information

A Biswas, Apratim Guha

Research output: Contribution to journalArticle

10 Citations (Scopus)


Despite its importance, there has been little attention in the modeling of time series data of categorical nature in the recent past. In this paper, we present a framework based on the Pegram's [An autoregressive model for multilag Markov chains. Journal of Applied Probabability 17, 350-362] operator that was originally proposed only to construct discrete AR(p) processes. We extend the Pegram's operator to accommodate categorical processes with ARMA representations. We observe that the concept of correlation is not always suitable for categorical data. As a sensible alternative, we use the concept of mutual information, and introduce auto-mutual information to define the time series process of categorical data. Some model selection and inferential aspects are also discussed. We implement the developed methodologies to analyze a time series data set on infant sleep status. (C) 2008 Elsevier B.V. All rights reserved,
Original languageEnglish
Pages (from-to)3076-3087
Number of pages12
JournalJournal of Statistical Planning and Inference
Issue number9
Publication statusPublished - 1 Sept 2009


  • Partial auto-correlation function
  • Maximum likelihood estimates
  • Auto-correlation function
  • Thinning operator
  • Mixture distribution
  • Mutual information


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