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.

Time Series Modelling

“…Properties of, and estimation for, this new type of INMA model are investigated, and they are illustrated by an application to a crime-counts time series. While the three aforementioned articles consider stationary and linear count time series, the contribution by Liu et al [ 14 ] deals with non-stationary and non-linear time series as obtained from the periodic self-exciting threshold INAR model. Properties and estimation are discussed, and an application to monthly counts of claimants is presented.…”