Detection of Changes in Multivariate Time Series With Application to EEG Data

Abstract

The primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series. We extend the class of score type change point statistics considered in 2007 by Hušková, Prášková, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative. Our proposed procedures do not require the observed time series to actually follow the VAR model. Instead, following the strategy implicitly employed by practitioners, our approach takes model misspecification into account so that our detection procedure uses the model background merely for feature extraction. We derive the asymptotic distributions of our test statistics and show that our procedure has asymptotic power of 1. The proposed test statistics require the estimation of the inverse of the long-run covariance matrix which is particularly difficult in higher-dimensional settings (i.e., where the dimension of the time series and the dimension of the parameter vector are both large). Thus we robustify the proposed test statistics and investigate their finite sample properties via extensive numerical experiments. Finally, we apply our procedure to electroencephalograms and demonstrate its potential impact in identifying change points in complex brain processes during a cognitive motor task.

• Change points
• Epidemic change
• Vector autoregressive model

Additional information

Notes on contributors

Claudia Kirch

Claudia Kirch is Professor, Institute for Mathematical Stochastics at the Otto von Guericke University Magdeburg, PF 4120, 39016 Magdeburg (E-mail: [email protected]). Birte Muhsal, Institute of Stochastics at the Karlsruhe Institute of Technology (KIT), Kaiserstr. 89, 76133 Karlsruhe, Germany (E-mail: [email protected]). Hernando Ombao is Professor, Department of Statistics, University of California at Irvine, Irvine CA 92697, USA (E-mail: [email protected]).

Birte Muhsal

Claudia Kirch is Professor, Institute for Mathematical Stochastics at the Otto von Guericke University Magdeburg, PF 4120, 39016 Magdeburg (E-mail: [email protected]). Birte Muhsal, Institute of Stochastics at the Karlsruhe Institute of Technology (KIT), Kaiserstr. 89, 76133 Karlsruhe, Germany (E-mail: [email protected]). Hernando Ombao is Professor, Department of Statistics, University of California at Irvine, Irvine CA 92697, USA (E-mail: [email protected]).

Hernando Ombao

Claudia Kirch is Professor, Institute for Mathematical Stochastics at the Otto von Guericke University Magdeburg, PF 4120, 39016 Magdeburg (E-mail: [email protected]). Birte Muhsal, Institute of Stochastics at the Karlsruhe Institute of Technology (KIT), Kaiserstr. 89, 76133 Karlsruhe, Germany (E-mail: [email protected]). Hernando Ombao is Professor, Department of Statistics, University of California at Irvine, Irvine CA 92697, USA (E-mail: [email protected]).