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

Claudia Kirch, Birte Muhsal, Hernando Ombao

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1197-1216
Number of pages20
JournalJournal of the American Statistical Association
Volume110
Issue number511
DOIs
StatePublished - Jul 3 2015

Keywords

  • Change points
  • Epidemic change
  • Vector autoregressive model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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