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 language | English |
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Pages (from-to) | 207-229 |
Number of pages | 23 |
Journal | Statistica Sinica |
Volume | 22 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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