Monitoring mean changes in persistent multivariate time series

ABSTRACT

We focus on sequential (online) monitoring of changes in the mean vector of high-dimensional persistent VARMA time series by using multivariate control charts. Applying either modified or residual control charts to the original process or to the process of VARMA residuals could be problematic when the degree of autoregressive persistence is high. To overcome these difficulties, we suggest to monitor the process of the vector first differences of the VARMA series. We derive the stochastic properties of this difference vector process which are required for the design of the multivariate control charts. Then, we illustrate the performance of our approach in a Monte Carlo simulation study for detection of various types of mean changes.

KEYWORDS:

• Multiple time series
• multivariate control charts
• online monitoring
• VARMA

Acknowledgements

We thank two anonymous referees for providing constructive comments which helped to improve our paper.

Disclosure statement

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

Notes

The smallest out-of-control ARLs are marked in bold.

The smallest out-of-control ARLs are marked in bold.

Additional information

Funding

This work has been partly supported by the Collaborative Research Center ‘Statistical Modeling of Nonlinear Dynamic Processes’ (SFB 823, Project A1) of the German Research Foundation (DFG).