On the asymptotic behaviour of the eigenvalue distribution of block correlation matrices of high-dimensional time series

2020/04/15 by Philippe Loubaton, Loubaton, Philippe, Xavier Mestre +1
Mathematics · Physics and Astronomy · #60B20 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2004.07226

openalex publication_date 2020/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of M mutually independent scalar time series. This matrix is composed of M × M blocks that contain the sample cross correlation between pairs of time series. In particular, each block has size L × L and contains the sample cross-correlation measured at L consecutive time lags between each pair of time series. Let N denote the total number of consecutively observed windows that are used to estimate these correlation matrices. We analyze the asymptotic regime where M,L,N → +∞ while ML/N → c_⋆, 0

Citations

• Large random matrix approach for testing independence of a large number of Gaussian time series

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