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

Philippe Loubaton, Alexis Rosuel and Pascal Vallet

Journal of Multivariate Analysis, 2023, vol. 194, issue C

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 MN→0 and MB→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.

Keywords: High dimensional statistics; Independence test; Spectral analysis; Time series (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2022.105124

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