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Article

A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors

by
Huaping Chen
1,*,
Fukang Zhu
2 and
Xiufang Liu
3
1
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
2
School of Mathematics, Jilin University, Changchun 130012, China
3
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
*
Author to whom correspondence should be addressed.
Stats 2022, 5(3), 819-840; https://doi.org/10.3390/stats5030048
Submission received: 11 July 2022 / Revised: 15 August 2022 / Accepted: 15 August 2022 / Published: 19 August 2022
(This article belongs to the Section Time Series Analysis)
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Abstract

Recently, there has been a growing interest in integer-valued time series models, especially in multivariate models. Motivated by the diversity of the infinite-patch metapopulation models, we propose an extension to the popular bivariate INAR(1) model, whose innovation vector is assumed to be time-dependent in the sense that the mean of the innovation vector is linearly increased by the previous population size. We discuss the stationarity and ergodicity of the observed process and its subprocesses. We consider the conditional maximum likelihood estimate of the parameters of interest, and establish their large-sample properties. The finite sample performance of the estimator is assessed via simulations. Applications on crime data illustrate the model.
Keywords: bivariate INAR model; bivariate poisson distribution; time-dependent innovation; time series of counts; stability; parameters estimation bivariate INAR model; bivariate poisson distribution; time-dependent innovation; time series of counts; stability; parameters estimation

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MDPI and ACS Style

Chen, H.; Zhu, F.; Liu, X. A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors. Stats 2022, 5, 819-840. https://doi.org/10.3390/stats5030048

AMA Style

Chen H, Zhu F, Liu X. A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors. Stats. 2022; 5(3):819-840. https://doi.org/10.3390/stats5030048

Chicago/Turabian Style

Chen, Huaping, Fukang Zhu, and Xiufang Liu. 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors" Stats 5, no. 3: 819-840. https://doi.org/10.3390/stats5030048

APA Style

Chen, H., Zhu, F., & Liu, X. (2022). A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors. Stats, 5(3), 819-840. https://doi.org/10.3390/stats5030048

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