On bivariate threshold Poisson integer-valued autoregressive processes

To capture the bivariate count time series showing piecewise phenomena, we introduce a first-order bivariate threshold Poisson integer-valued autoregressive process. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares and conditional maximum likelihood estimators, as well as their asymptotic properties, are obtained for both the cases that the threshold parameter is known or not. A new algorithm to estimate the threshold parameter of the model is also provided. Moreover, the nonlinearity test and forecasting problems are also addressed. Finally, some numerical results of the estimates and a real data example are presented.