Multiscale and multilevel technique for consistent segmentation of nonstationary time series

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. keywords: binary segmentation, breakpoint detection, locally stationary wavelet model, piecewise stationarity, post-processing, wavelet periodogram. ∗Department of Statistics, London School of Economics, UK. E-mail: [email protected], Phone: +44 (0)20 7955 6014, Fax: +44 (0)20 7955 7416 †Department of Statistics, London School of Economics, UK. E-mail: [email protected]