Abstract
In this paper, we introduce a class of periodic negative binomial self-exciting threshold integer-valued autoregressive model. The basic probabilistic and statistical properties of this class are studied. Furthermore, the existence of a high moment and the strict periodic stationarity as well as the ergodicity, are established. The periodic autocovariance structure is also considered. The Conditional Least Squares (CLS) 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 parameter. The asymptotic properties of the estimators are obtained. The performance of the CLS and the CML are compared through an intensive simulation study. An application on a real data set is provided.
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