Segmenting Low- and High-Dimensional Time Series via Binary Segmentation and Its Modern Variants

• Activity Number: 443
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Haeran Cho and Piotr Fryzlewicz*+
• Companies: London School of Economics and London School of Economics
• Keywords: change-point detection ; CUSUM ; wavelets ; time series ; binary segmentation ; high dimensionality

Abstract

We propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of change-points. 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 change-points in wavelet periodograms 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 change-points in the second-order structure of the original process. An extensive simulation study demonstrates good performance of our method. We also present a more recent extension of our technique to a multivariate setting with a possibly large number of time series, as well as an improved "wild" version of the binary segmentation procedure.