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arXiv · 1611.09727

Multiscale and multilevel technique for consistent segmentation of nonstationary time series

Haeran Cho·Piotr Fryzlewicz
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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 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 breakpoints in the second-order structure of the original process. An extensive simulation study demonstrates good performance of our method.

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Haeran Cho, Piotr Fryzlewicz. 2016-11-29. Multiscale and multilevel technique for consistent segmentation of nonstationary time series. https://doi.org/10.5705/ss.2009.280

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