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Auto-association measures for stationary time series of categorical data

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  • Atanu Biswas
  • Maria Carmen Pardo
  • Apratim Guha

Abstract

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, 2009a ) 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

Suggested Citation

  • Atanu Biswas & Maria Carmen Pardo & Apratim Guha, 2014. "Auto-association measures for stationary time series of categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 487-514, September.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:3:p:487-514
    DOI: 10.1007/s11749-014-0364-8
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    References listed on IDEAS

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    1. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    2. Maiti, Raju & Biswas, Atanu & Guha, Apratim & Seng, Huat Ong, 2013. "Modelling and coherent forecasting of zero-inflated time series count data," IIMA Working Papers WP2013-05-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. 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.
    4. 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.
    5. Biswas, Atanu & Song, Peter X.-K., 2009. "Discrete-valued ARMA processes," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1884-1889, September.
    6. Luca Bagnato & Antonio Punzo & Orietta Nicolis, 2012. "The autodependogram: a graphical device to investigate serial dependences," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 233-254, March.
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    Cited by:

    1. Apratim Guha & Atanu Biswas & Abhik Ghosh, 2021. "A nonparametric two‐sample test using a general φ‐divergence‐based mutual information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 180-202, May.

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