Gradual change-point analysis based on Spearman matrices for multivariate time series

It may happen that the behavior of a multivariate time series is such that the underlying joint distribution is gradually moving from one distribution to another between unknown times of change. Under this context of a possible gradual-change, tests of change-point detection in the dependence struct...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics 2024-06, Vol.76 (3), p.423-446
Main Author: Quessy, Jean-François
Format: Article
Language:English
Subjects:
Economics
Finance
Insurance
Management
Mathematics and Statistics
Multivariate analysis
Statistical tests
Statistics
Statistics for Business
Synthetic data
Time series
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Summary:It may happen that the behavior of a multivariate time series is such that the underlying joint distribution is gradually moving from one distribution to another between unknown times of change. Under this context of a possible gradual-change, tests of change-point detection in the dependence structure of multivariate series are developed around the associated sequence of Spearman matrices. It is formally established that the proposed test statistics for that purpose are asymptotically marginal-free under a general strong-mixing assumption, and written as functions of integrated Brownian bridges. Consistent estimators of the pair of times of change, as well as of the before-the-change and after-the-change Spearman matrices, are also proposed. A simulation study examines the sampling properties of the introduced tools, and the methodologies are illustrated on a synthetic dataset.
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-023-00891-5