Counting distinct multivariate self-similarity parameters using a bootstrap-driven graph clustering approach
Résumé
In various modern fields, the multiplicity of sensors in applications may result in potentially numerous scale-free time series that jointly characterize one same system. Multivariate self-similarity analysis tackles the challenge of studying these systems by providing as many self-similarity parameter estimates as available time series. The possibly large amount of self-similarity parameters raises the major issue of identifying the number of actually distinct self-similarity parameters. The present work attains this goal by designing an adapted graph to perform a spectral clustering-type procedure. The proposed graph is weighted using pairwise equality test p-values estimated by a multivariate time-scale block-bootstrap scheme combined with wavelet random matrix eigenanalysis for self-similarity parameter estimation. Numerical experiments on synthetic multivariate data show a very satisfactory performance of the clustering strategy.
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