On a periodic SETINAR model

In this paper, we study a class of periodic self-exciting threshold integer-valued autoregressive model. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed-forms of these moments are, under the obtained conditions, derived. Furthermore, the existence of high moment and the strict periodic stationarity so that the ergodicity, are established. The periodic autocovariance structure is also considered. The Conditional Least Squares and the Conditional Maximum Likelihood (CML) methods are applied to estimate the underlying parameters, while using the periodic adaptation of the Nested Sub-Sample Search (NeSS) algorithm, to estimate the periodic threshold parameters. The asymptotic properties of the estimators are obtained. The performance of the Conditional Least Squares (CLS) and the Conditional Maximum Likelihood (CML) are compared through a simulation study. Finally, an application on a real data set is provided.