High-order self-excited multiple thresholds generalized integer-valued autoregressive model

This work proposes an integer threshold autoregressive model with multiple regimes $\left( K\geq2\right)$, based on a generalized thinning operator (hereafter referred to as $SET-GINAR\left( K;p\right)$). This model will be useful for analyzing the number of certain arrivals in a fixed time interval with non-linear behavior. First, we study the probabilistic structure of our model through the stationarity issue and the moments structure. Second, we provide two statistical inference procedures, namely two estimation methods including the conditional least squares and the conditional maximum likelihood. In addition, the asymptotic properties of the estimators, including consistency and normality, are established. Finally, the performance of the obtained inference procedures will be evaluated through an intensive simulation study and application on real data.