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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Vydáno v:	Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 77; číslo 2; s. 475 - 507
Hlavní autoři:	Cho, Haeran, Fryzlewicz, Piotr
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Royal Statistical Society 01.03.2015 Blackwell Publishing Ltd John Wiley & Sons Ltd Oxford University Press
Témata:	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
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Shrnutí:	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.
Bibliografie:	http://dx.doi.org/10.1111/rssb.12079 ark:/67375/WNG-BZQNSVCF-7 istex:FEAD5F63FD3724A1F2D837E9F94008CE22609A5F ArticleID:RSSB12079 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	1369-7412 1467-9868
DOI:	10.1111/rssb.12079