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

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).