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Measures of Dispersion and Serial Dependence in Categorical Time Series

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  • Christian H. Weiß

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

Abstract

The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. Regarding signed serial dependence in categorical time series, we consider three types of κ -measures. By analyzing bias properties, it is shown that always one of the κ -measures is related to one of the above-mentioned dispersion measures. For doing statistical inference based on the sample versions of these dispersion and dependence measures, knowledge on their distribution is required. Therefore, we study the asymptotic distributions and bias corrections of the considered dispersion and dependence measures, and we investigate the finite-sample performance of the resulting asymptotic approximations with simulations. The application of the measures is illustrated with real-data examples from politics, economics and biology.

Suggested Citation

  • Christian H. Weiß, 2019. "Measures of Dispersion and Serial Dependence in Categorical Time Series," Econometrics, MDPI, vol. 7(2), pages 1-23, April.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:2:p:17-:d:224845
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    References listed on IDEAS

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    1. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
    2. Christian Weiß & Rainer Göb, 2008. "Measuring serial dependence in categorical time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 71-89, February.
    3. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-1024, September.
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