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A bivariate integer-valued bilinear autoregressive model with random coefficients

Author

Listed:
  • Predrag M. Popović

    (University of Niš)

  • Hassan S. Bakouch

    (Tanta University)

Abstract

This paper introduces a new bivariate autoregressive model with random coefficients for the time series of counts. It is composed of two components, the survival and the innovation component. The dependence between two series that comprise the bivariate model stems from both of these components. The introduced model is achieved by defining a bilinear model and the existence of a unique strict stationarity of it is proved. The method of moments is examined for parameters estimation. The practical aspect of the model is discussed by using a real-life data example.

Suggested Citation

  • Predrag M. Popović & Hassan S. Bakouch, 2020. "A bivariate integer-valued bilinear autoregressive model with random coefficients," Statistical Papers, Springer, vol. 61(5), pages 1819-1840, October.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:5:d:10.1007_s00362-018-1005-1
    DOI: 10.1007/s00362-018-1005-1
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    References listed on IDEAS

    as
    1. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    2. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    3. Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
    4. Quinn, B. G., 1982. "Stationarity and invertibility of simple bilinear models," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 225-230, March.
    5. Shiqing Ling & Liang Peng & Fukang Zhu, 2015. "Inference For A Special Bilinear Time-Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 61-66, January.
    6. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    7. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    8. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    9. Aleksandar S. Nastić & Petra N. Laketa & Miroslav M. Ristić, 2016. "Random environment integer-valued autoregressive process," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 267-287, March.
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    Full references (including those not matched with items on IDEAS)

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