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.

Keywords:

• Time series of counts
• mean targeting estimation
• INGARCH model
• exponential family
• change point test

Acknowledgements

We thank the Editor, an AE, and one anonymous referee for their valuable comments.

Additional information

Funding

This research is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning (No. 2018R1A2A2A05019433).