Two-step conditional least squares estimation for the bivariate Z-valued INAR(1) model with bivariate Skellam innovations

Huaping Chen, Fukang Zhu and Xiufang Liu

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 11, 4085-4106

Abstract: This article studies the two-step conditional least squares (CLS) estimation for the bivariate Z-valued INAR(1) model with bivariate Skellam innovations. For readers’ convenience, we first give a brief review of the bivariate Skellam distribution, bivariate signed thinning operator and the definition of the bivariate Z-valued INAR(1) model with bivariate Skellam innovations (denoted as the BSK-BINARS(1) model). Then, we discuss the stationarity and ergodicity of the BSK-BINARS(1) model, give some stochastic properties. Second, we discuss the two-step CLS estimate of the parameters and establish their large-sample properties. Third, we conduct a simulation study to illustrate the finite sample performances of the two-step CLS estimators, which are compared with those obtained by the plug-in method. Last but not least, we apply the BSK-BINARS(1) model on the zonal annual means temperature (*100).

Date: 2024
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DOI: 10.1080/03610926.2023.2172587

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