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Statistical analysis of discrete-valued time series using categorical ARMA models

Author

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  • Song, Peter X.-K.
  • Freeland, R. Keith
  • Biswas, Atanu
  • Zhang, Shulin

Abstract

This paper concerns the analysis of discrete-valued time series using a class of categorical ARMA models recently proposed by Biswas and Song (2009). Such ARMA processes are flexible to model discrete-valued time series, allowing a wide range of marginal distributions such as binomial, multinomial, Poisson and nominal/ordinal categorical probability mass functions. To apply these models in the data analysis this paper focuses on the development of a needed statistical toolbox, which includes maximum likelihood estimation and inference, model selection, and goodness-of-fit test. Particularly in AR models a bias-corrected AIC statistic is derived for the order selection, while a randomized conditional moment (RCM) test is furnished to examine the goodness-of-fit. Finite-sample performances of the proposed methods are examined through simulation studies, in which the bias-corrected AIC is shown to outperform the traditional AIC and BIC statistics and the RCM test achieves desirable power. As part of the numeric illustration, a data analysis of categorical time series on infant sleep quality is provided by the application of this new toolbox.

Suggested Citation

  • Song, Peter X.-K. & Freeland, R. Keith & Biswas, Atanu & Zhang, Shulin, 2013. "Statistical analysis of discrete-valued time series using categorical ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 112-124.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:112-124
    DOI: 10.1016/j.csda.2012.06.003
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    References listed on IDEAS

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    1. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
    2. Biswas, Atanu & Song, Peter X.-K., 2009. "Discrete-valued ARMA processes," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1884-1889, September.
    3. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
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    7. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    8. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    9. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    10. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
    11. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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    Cited by:

    1. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.

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