Mean targeting estimation for integer-valued time series with application to change point test

Abstract

This study considers the mean targeting estimation for integer-valued time series models and a parameter change test as its application. We first introduce the mean targeting quasi-maximum likelihood estimator (QMLE) based on generalized autoregressive conditional heteroscedastic (INGARCH) models and then consider the CUSUM test of (standardized) residuals. To evaluate the performance, we conduct a Monte Carlo simulation study applying a negative binomial mean targeting QMLE to Poisson INGARCH, Poisson integer-valued autoregressive (INAR), and log-linear Poisson INGARCH times series of counts, and demonstrate its validity. A real data analysis is also conducted using the drug offense data in Pittsburgh and Goldman Sachs Group stock data for illustration.