Correlation tests and sample spectral coherence matrix in the high-dimensional regime
Résumé
It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n∈Z with independent components satisfy at each frequency a central limit theorem in the asymptotic regime where the sample size N , the dimension M of the observation, and the smoothing span B both converge towards +∞ in such a way that M = O(N α ) for α < 1 and M B → c, c ∈ (0, 1). It is deduced that two recentered and renormalized versions of the LSS, one based on an average in the frequency domain and the other one based on a sum of squares also in the frequency domain, and both evaluated over a well-chosen frequency grid, also verify a central limit theorem. These two statistics are proposed to test with controlled asymptotic level the hypothesis that the components of y are independent. Numerical simulations assess the performance of the two tests.
Mots clés
- secondary 62M15 High-dimensional time series large random matrices spectral coherence matrix independence test
- large random matrices
- secondary 62M15 High-dimensional time series
- Primary 60B20
- Primary 60B20 62H15
- secondary 62M15 Large random matrices
- 62H15
- MSC2020 subject classifications: Primary 60B20
- secondary 62M15 Large random matrices high-dimensional time series spectral coherence matrix independence test
- MSC2020 subject classifications: Primary 60B20 62H15
- Large random matrices
- independence test
- spectral coherence matrix
- high-dimensional time series
Domaines
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