Multiscale and multilevel technique for consistent segmentation of nonstationary time series

Haeran Cho*, Piotr Fryzlewicz

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

27 Citations (Scopus)

Abstract

In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary Wavelet model, in which a complete description of the piecewise-stationary second-order structure is provided by wavelet periodograms computed at multiple scales and locations. The initial stage of our method is a new binary segmentation procedure, with a theoretically justified and rapidly computable test criterion that detects breakpoints in wavelet periodograrns separately at each scale. This is followed by within-scale and across-scales post-processing steps, leading to consistent estimation of the number and locations of breakpoints in the second-order structure of the original process. An extensive simulation study demonstrates good performance of our method.

Original languageEnglish
Pages (from-to)207-229
Number of pages23
JournalStatistica Sinica
Volume22
Issue number1
DOIs
Publication statusPublished - Jan 2012

Keywords

  • EVOLUTIONARY WAVELET SPECTRA
  • SEQUENCE
  • Binary segmentation
  • wavelet periodogram
  • CHANGE-POINT
  • SHIFTS
  • ADAPTIVE ESTIMATION
  • post-processing
  • locally stationary wavelet model
  • piecewise stationarity
  • VARIANCE
  • LOCATION
  • MEMORY
  • SQUARES
  • breakpoint detection
  • MODELS

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