Monitoring parameter shift with Poisson integer-valued GARCH models

ABSTRACT

This study examines the statistical process control chart used to detect a parameter shift with Poisson integer-valued GARCH (INGARCH) models and zero-inflated Poisson INGARCH models. INGARCH models have a conditional mean structure similar to GARCH models and are well known to be appropriate to analyzing count data that feature overdispersion. Special attention is paid in this study to conditional and general likelihood ratio-based (CLR and GLR) CUSUM charts and the score function-based CUSUM (SFCUSUM) chart. The performance of each of the proposed methods is evaluated through a simulation study, by calculating their average run length. Our findings show that the proposed methods perform adequately, and that the CLR chart outperforms the GLR chart when there is an increased shift of parameters. Moreover, the use of the SFCUSUM chart in particular is found to lead to a lower false alarm rate than the use of the CLR chart.

KEYWORDS:

• Time series of counts
• ZIP INGARCH model
• statistical process control
• likelihood ratio-based control chart
• score function-based CUSUM chart
• false alarm rate

Acknowledgements

We would like to thank an anonymous referee for his/her careful reading and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work 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. 2015R1A2A2A010003894).