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Measuring serial dependence in categorical time series

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An intrinsic feature of a time series is that, typically, adjacent observations are dependent. The nature of this dependence among observations of a time series is of considerable practical interest. Time series analysis is concerned with techniques for the analysis of this dependence. (Box et al. 1994p. 1)

Abstract

The analysis of time-indexed categorical data is important in many fields, e.g., in telecommunication network monitoring, manufacturing process control, ecology, etc. Primary interest is in detecting and measuring serial associations and dependencies in such data. For cardinal time series analysis, autocorrelation is a convenient and informative measure of serial association. Yet, for categorical time series analysis an analogous convenient measure and corresponding concepts of weak stationarity have not been provided. For two categorical variables, several ways of measuring association have been suggested. This paper reviews such measures and investigates their properties in a serial context. We discuss concepts of weak stationarity of a categorical time series, in particular of stationarity in association measures. Serial association and weak stationarity are studied in the class of discrete ARMA processes introduced by Jacobs and Lewis (J. Time Ser. Anal. 4(1):19–36, 1983).

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Authors and Affiliations

  1. Institute of Mathematics, Department of Statistics, University of Würzburg, Würzburg, Germany

    Christian H. Weiß & Rainer Göb

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  1. Christian H. Weiß
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  2. Rainer Göb
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Correspondence to Christian H. Weiß.

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Weiß, C.H., Göb, R. Measuring serial dependence in categorical time series. AStA 92, 71–89 (2008). https://doi.org/10.1007/s10182-008-0055-4

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  • DOI: https://doi.org/10.1007/s10182-008-0055-4

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