On residual CUSUM statistic for PINAR(1) model in statistical design and diagnostic of control chart

Abstract

This paper studies the residual-based CUSUM test statistic in first-order Poisson integer-valued autoregressive (PINAR(1)) models. The residuals are calculated with squared difference (SD) estimates, and a retrospective phase (Phase I) analysis is conducted. Moreover, the upper one-sided CUSUM-type chart (RCUSUMV chart) is considered for effectively detecting abnormal shifts in a monitoring phase (Phase II) situation. Numerical experiments show that our method can be good alternative to conventional CUSUM charts when an effective detection and accurate change point estimation for small shifts are primary concerns.

Keywords:

• INAR(1)
• CUSUM test
• Statistical process control
• CUSUM chart
• Average run length
• Change point analysis

Acknowledgements

We thank the referee for his/her careful reading and 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).