| Issue |
EPL
Volume 129, Number 6, March 2020
|
|
|---|---|---|
| Article Number | 60003 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/129/60003 | |
| Published online | 21 April 2020 | |
Eigenvalue and eigenvector statistics in time series analysis
1 Department of Computer Science, University College London - London WC1E 6EA, UK
2 Faculty of Physics, Bielefeld University - P.O. Box 100131, D-33501 Bielefeld, Germany
3 School of Mathematical Sciences, University of Nottingham - Nottingham NG7 2RD, UK
Received: 14 October 2019
Accepted: 7 April 2020
The study of correlated time series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of complex systems. Despite this fact, no general result is known for the statistics of eigenvectors of the cross-correlations of correlated time series. Here we use supersymmetric theory to provide novel analytical results that will serve as a benchmark for the study of correlated signals for a vast community of researchers.
PACS: 05.45.Tp – Time series analysis / 02.10.Yn – Matrix theory / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2020
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