Affordable Access

On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime

Authors
  • Rosuel, Alexis
  • Loubaton, Philippe
  • Vallet, Pascal
Publication Date
Jun 23, 2021
Source
HAL-Ecole des Ponts ParisTech
Keywords
Language
English
License
Unknown
External links

Abstract

We investigate the asymptotic distribution of the maximum of a frequency smoothed estimate of the spectral coherence of a M-variate complex Gaussian time series with mutually independent components when the dimension M and the number of samples N both converge to infinity. If B denotes the smoothing span of the underlying smoothed periodogram estimator, a type I extreme value limiting distribution is obtained under the rate assumptions M N → 0 and M B → c ∈ (0, +∞). This result is then exploited to build a statistic with controlled asymptotic level for testing independence between the M components of the observed time series. Numerical simulations support our results.

Report this publication

Statistics

Seen <100 times