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INAR approximation of bivariate linear birth and death process

Chen, Zezhun Chen, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Tzougas, George (2023) INAR approximation of bivariate linear birth and death process. Journal of Applied Statistics, 26 (3). 459 - 497. ISSN 0266-4763

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Identification Number: 10.1007/s11203-023-09289-9


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.

Item Type: Article
Additional Information: © 2023 The Author(s)
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 02 May 2023 09:51
Last Modified: 19 May 2024 06:45

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