A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors
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.
Academic Editor: Wei Zhu
Stats 2022, 5(3), 819-840; https://doi.org/10.3390/stats5030048
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)
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.
View Full-Text
Keywords:
bivariate INAR model; bivariate poisson distribution; time-dependent innovation; time series of counts; stability; parameters estimation
▼
Show Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 StyleChen, 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
Find Other Styles
