Exponential family QMLE-based CUSUM test for integer-valued time series

Abstract

This study considers testing for parameter changes in integer-valued time series models based on one parameter exponential family quasi-maximum likelihood estimates. We employ the cumulative sum (CUSUM) test as a change point test, based on score vectors, residuals, standardized residuals, and squares of residuals, focusing on performance comparison of negative binomial (NB) quasi-maximum likelihood estimate (QMLE)-based tests. Monte Carlo simulations are conducted with Poisson, NB, zero-inflated Poisson and NB, generalized Poisson INGARCH(1,1) models and Poisson and NB INAR(1) models. Real data analysis using the Korean stock price index (KOSPI) 200 is also included for illustration. The findings validate QMLE-based CUSUM tests using standardized residuals for INGARCH models and residuals for INAR models. Zero proportional change is well detected by the test using squares of residuals.