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A Binomial Integer-Valued ARCH Model

Author

Listed:
  • Ristić Miroslav M.

    (Department of Mathematics, University of Niš, Niš, Serbia)

  • Weiß Christian H.

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

  • Janjić Ana D.

    (Department of Mathematics, University of Niš, Niš, Serbia)

Abstract

We present an integer-valued ARCH model which can be used for modeling time series of counts with under-, equi-, or overdispersion. The introduced model has a conditional binomial distribution, and it is shown to be strictly stationary and ergodic. The unknown parameters are estimated by three methods: conditional maximum likelihood, conditional least squares and maximum likelihood type penalty function estimation. The asymptotic distributions of the estimators are derived. A real application of the novel model to epidemic surveillance is briefly discussed. Finally, a generalization of the introduced model is considered by introducing an integer-valued GARCH model.

Suggested Citation

  • Ristić Miroslav M. & Weiß Christian H. & Janjić Ana D., 2016. "A Binomial Integer-Valued ARCH Model," The International Journal of Biostatistics, De Gruyter, vol. 12(2), pages 1-21, November.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:2:p:21:n:6
    DOI: 10.1515/ijb-2015-0051
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    References listed on IDEAS

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    1. Ruey S. Tsay, 1992. "Model Checking Via Parametric Bootstraps in Time Series Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 1-15, March.
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