INAR approximation of bivariate linear birth and death process

Zezhun Chen (), Angelos Dassios () and George Tzougas ()
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Zezhun Chen: London School of Economics and Political Science
Angelos Dassios: London School of Economics and Political Science
George Tzougas: Heriot-Watt University

Statistical Inference for Stochastic Processes, 2023, vol. 26, issue 3, No 1, 459-497

Abstract: 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.

Keywords: Bivariate birth and death; Linear birth and death; Integer-valued autoregressive of order one; Convergence in distribution; Discrete approximation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11203-023-09289-9

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