Statistical Inference for Periodic Self-Exciting Threshold Integer-Valued Autoregressive Processes

Abstract

This paper considers the periodic self-exciting threshold integer-valued autoregressive processes under a weaker condition in which the second moment is finite instead of the innovation distribution being given. The basic statistical properties of the model are discussed, the quasi-likelihood inference of the parameters is investigated, and the asymptotic behaviors of the estimators are obtained. Threshold estimates based on quasi-likelihood and least squares methods are given. Simulation studies evidence that the quasi-likelihood methods perform well with realistic sample sizes and may be superior to least squares and maximum likelihood methods. The practical application of the processes is illustrated by a time series dataset concerning the monthly counts of claimants collecting short-term disability benefits from the Workers’ Compensation Board (WCB). In addition, the forecasting problem of this dataset is addressed.

Keywords

• periodic autoregression
• integer-valued threshold models
• parameter estimation