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Pré-Publication, Document De Travail Année : 2021

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

Alexis Rosuel
Philippe Loubaton
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Résumé

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.
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Dates et versions

hal-03268401 , version 1 (23-06-2021)

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  • HAL Id : hal-03268401 , version 1

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Alexis Rosuel, Philippe Loubaton, Pascal Vallet. On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime. 2021. ⟨hal-03268401⟩
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