Multiple-change-point detection for high dimensional time series via sparsified binary segmentation

• 成果类型: Article
• 署名作者: Cho, Haeran; Fryzlewicz, Piotr
• 署名单位: University of Bristol; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12079
• 发表日期: 2015
• 页码: 475-507
• 关键词: break detection; dependence; squares

摘要

Time series segmentation, which is also known as multiple-change-point detection, is a well-established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second-order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms and cross-periodograms of the components of the input time series. However, the standard maximum' and average' methods for doing so often fail in high dimensions when, for example, the change points are sparse across the panel or the cumulative sum statistics are spuriously large. We propose the sparsified binary segmentation algorithm which aggregates the cumulative sum statistics by adding only those that pass a certain threshold. This sparsifying' step reduces the influence of irrelevant noisy contributions, which is particularly beneficial in high dimensions. To show the consistency of sparsified binary segmentation, we introduce the multivariate locally stationary wavelet model for time series, which is a separate contribution of this work.