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

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  • Loubaton, Philippe
  • Rosuel, Alexis
  • Vallet, Pascal

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.

Suggested Citation

  • Loubaton, Philippe & Rosuel, Alexis & Vallet, Pascal, 2023. "On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:jmvana:v:194:y:2023:i:c:s0047259x22001154
    DOI: 10.1016/j.jmva.2022.105124
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    References listed on IDEAS

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