Monitoring parameter change for time series models with application to location-Scale heteroscedastic models

Abstract

In this study, we consider an on-line monitoring procedure to detect a parameter change in general time series models, featuring location-scale heteroscedastic time series models and their conditional quantiles. To resolve this statistical process control (SPC) problem, we employ a residual-based cumulative sum (CUSUM) process specially designed to effectively detect both upward and downward changes in the conditional mean, variance, and quantiles of time series. To attain control limits analytically, limit theorems are provided for the proposed CUSUM monitoring process. A simulation study and real data analysis are conducted to illustrate its validity empirically.

Keywords:

• Monitoring parameter change
• CUSUM monitoring
• statistical process control
• location-scale time series models
• conditional quantiles

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

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 [grant number 2021R1A2C1004009].