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INAR approximation of bivariate linear birth and death process

Author

Listed:
  • Zezhun Chen

    (London School of Economics and Political Science)

  • Angelos Dassios

    (London School of Economics and Political Science)

  • George Tzougas

    (Heriot-Watt University)

Abstract

In this paper, we propose a new type of univariate and bivariate Integer-valued autoregressive model of order one (INAR(1)) to approximate univariate and bivariate linear birth and death process with constant rates. Under a specific parametric setting, the dynamic of transition probabilities and probability generating function of INAR(1) will converge to that of birth and death process as the length of subintervals goes to 0. Due to the simplicity of Markov structure, maximum likelihood estimation is feasible for INAR(1) model, which is not the case for bivariate and multivariate birth and death process. This means that the statistical inference of bivariate birth and death process can be achieved via the maximum likelihood estimation of a bivariate INAR(1) model.

Suggested Citation

  • Zezhun Chen & Angelos Dassios & George Tzougas, 2023. "INAR approximation of bivariate linear birth and death process," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 459-497, October.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09289-9
    DOI: 10.1007/s11203-023-09289-9
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    References listed on IDEAS

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    3. Forrest W. Crawford & Vladimir N. Minin & Marc A. Suchard, 2014. "Estimation for General Birth-Death Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 730-747, June.
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