Breakpoint Detection of Nonstationary Time Series Using Wild Binary Segmentation

• Activity Number: 644
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Karolos Korkas*+ and Piotr Fryzlewicz
• Companies: and London School of Economics
• Keywords: Binary Segmentation ; Random Design ; Piecewise Stationarity ; Wavelet Periodogram ; Locally Stationary Wavelets ; Post-processing

Abstract

We propose a new technique for consistent estimation of the breakpoints of a linear time series where the number and locations are unknown using the Wild Binary Segmentation (WBS) of Fryzlewicz (2012). We adopt the nonparametric Locally Stationary Wavelet model which provides a description of the second-order structure of a piecewise-stationary process through wavelet periodograms estimated at multiple scales and locations. The advantage of WBS is its localisation feature which means that it works in cases where the spacings between breakpoints are very short. In addition, we improve the performance of the algorithm by combining the breakpoints estimated from different scales and by using a post-processing step to eliminate spurious breakpoints. We finally provide an extensive simulation study to exhibit the good performance of the method.