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

arXiv: https://arxiv.org/abs/2107.02891 · HTML: https://mlsanity.com/paper/2107.02891/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [Bit Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/2412.12678/) (2024)

## Abstract (arXiv)

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 rightarrow 0 and M B rightarrow 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.