Multiple-change-point detection for high dimensional time series via sparsified binary segmentation

Haeran Cho*, Piotr Z Fryzlewicz

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

107 Citations (Scopus)
461 Downloads (Pure)

Abstract

Time series segmentation, which is also known as multiple-change-point detection, is a well-established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second-order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms and cross-periodograms of the components of the input time series. However, the standard 'maximum' and 'average' methods for doing so often fail in high dimensions when, for example, the change points are sparse across the panel or the cumulative sum statistics are spuriously large. We propose the sparsified binary segmentation algorithm which aggregates the cumulative sum statistics by adding only those that pass a certain threshold. This 'sparsifying' step reduces the influence of irrelevant noisy contributions, which is particularly beneficial in high dimensions. To show the consistency of sparsified binary segmentation, we introduce the multivariate locally stationary wavelet model for time series, which is a separate contribution of this work.

Original languageEnglish
Pages (from-to)475-507
Number of pages33
JournalJournal of the Royal Statistical Society B
Volume77
Issue number2
Early online date24 Jul 2014
DOIs
Publication statusPublished - Mar 2015

Keywords

  • Binary segmentation
  • Cumulative sum statistic
  • High dimensional time series
  • Locally stationary wavelet model
  • Multiple-change-point detection
  • Thresholding

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