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

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 ge...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 77; no. 2; pp. 475 - 507
Main Authors: Cho, Haeran, Fryzlewicz, Piotr
Format: Journal Article
Language:English
Published: Oxford Royal Statistical Society 01.03.2015
Blackwell Publishing Ltd
John Wiley & Sons Ltd
Oxford University Press
Subjects:
Algorithms
Averages
Binary segmentation
Changes
Cumulative sum statistic
Dimensionality
Economic crises
Hierarchical scales
High dimensional time series
International
Locally stationary wavelet model
Multiple-change-point detection
Multivariate analysis
Null hypothesis
Segmentation
Simulations
Standard and Poors 500 Index
Standard deviation
Statistical analysis
Statistics
Studies
Threshing
Thresholding
Time
Time series
time series analysis
Time series models
wavelet
United Kingdom > UK
ISSN:1369-7412, 1467-9868
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1111/rssb.12079
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12079