Statistical process monitoring for vector autoregressive time series based on location-scale CUSUM method

Abstract

In this study, we design a monitoring method for the vector autoregressive (VAR) and structural VAR (SVAR) time series using the residual-based cumulative sum (CUSUM) control chart. The residuals are calculated with a sequentially observed testing sample and the parameter estimates obtained from a training sample. Control limits are determined asymptotically when type 1 error probability scheme is used, but average run length (ARL) is also used in our empirical study. For the SVAR time series, independent component analysis (ICA) method is applied. A simulation study and real data analysis are conducted to evaluate our method.

Keywords:

• anomaly detection
• independent component analysis
• residual-based monitoring
• statistical process control
• (S)VAR time series

Acknowledgments

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

Additional information

Funding

This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) (No. 2021R1A2C1004009).

Notes on contributors

Sangjo Lee

Sangjo Lee is a PhD student of the Department of Statistics at Seoul National University. His research interests include multiple change point detection and statistical process control in time series analysis.

Sangyeol Lee

Sangyeol Lee is a professor of the Department of Statistics at Seoul National University. Prof. Lee received his doctorate in Statistics in 1991 at University of Maryland, College Park. His research areas include time series analysis, inference for stochastic processes, change point analysis, and statistical process control.