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Abstract Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.
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Fast and Scalable Algorithm for Detection of Structural Breaks in Big VAR Models
Many real time series datasets exhibit structural changes over time. A popular model for capturing their temporal dependence is that of vector autoregressions (VAR), which can accommodate structural changes through time evolving transition matrices. The problem then becomes to both estimate the (unknown) number of structural break points, together with the VAR model parameters. An additional challenge emerges in the presence of very large datasets, namely on how to accomplish these two objectives in a computational efficient manner. In this article, we propose a novel procedure which leverages a block segmentation scheme (BSS) that reduces the number of model parameters to be estimated through a regularized least-square criterion. Specifically, BSS examines appropriately defined blocks of the available data, which when combined with a fused lasso-based estimation criterion, leads to significant computational gains without compromising on the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with new local and exhaustive search steps to consistently estimate the number and relative location of the break points. The procedure is scalable to big high-dimensional time series datasets with a computational complexity that can achieve O(n), where n is the length of the time series (sample size), compared to an exhaustive procedure that requires steps. Extensive numerical work on synthetic data supports the theoretical findings and illustrates the attractive properties of the procedure. Finally, an application to a neuroscience dataset exhibits its usefulness in applications. Supplementary files for this article are available online.
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- PAR ID:
- 10312308
- Publisher / Repository:
- Taylor and Francis
- Date Published:
- Journal Name:
- Journal of Computational and Graphical Statistics
- ISSN:
- 1061-8600
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/10618600.2021.1950005
