期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 80, 期 1, 页码 57-83出版社
WILEY
DOI: 10.1111/rssb.12243
关键词
Change point estimation; Convex optimization; Dimension reduction; Piecewise stationary; Segmentation; Sparsity
资金
- Engineering and Physical Sciences Research Council
- Leverhulme Trust
- Alan Turing Institute
- Engineering and Physical Sciences Research Council [EP/J017213/1] Funding Source: researchfish
- EPSRC [EP/J017213/1] Funding Source: UKRI
Change points are a very common feature of big data' that arrive in the form of a data stream. We study high dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the co-ordinates. The challenge is to borrow strength across the co-ordinates to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called inspect for estimation of the change points: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimization problem derived from the cumulative sum transformation of the time series. We then apply an existing univariate change point estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated change points and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data-generating mechanisms. Software implementing the methodology is available in the R package InspectChangepoint.
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