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

IF 0.9 4区 数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2021-10-22 DOI:10.1142/s2010326322500241
P. Loubaton, X. Mestre
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引用次数: 1

Abstract

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of [Formula: see text] mutually independent scalar time series. This matrix is composed of [Formula: see text] blocks. Each block has size [Formula: see text] and contains the sample cross-correlation measured at [Formula: see text] consecutive time lags between each pair of time series. Let [Formula: see text] denote the total number of consecutively observed windows that are used to estimate these correlation matrices. We analyze the asymptotic regime where [Formula: see text] while [Formula: see text], [Formula: see text]. We study the behavior of linear statistics of the eigenvalues of this block correlation matrix under these asymptotic conditions and show that the empirical eigenvalue distribution converges to a Marcenko–Pastur distribution. Our results are potentially useful in order to address the problem of testing whether a large number of time series are uncorrelated or not.
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高维时间序列块相关矩阵特征值分布的渐近性
我们考虑从一组[公式:见文本]相互独立的标量时间序列的块归一化相关矩阵建立的线性谱统计。这个矩阵由[公式:见文本]块组成。每个块具有大小[公式:见文本],并且包含在[公式:见文本]处测量的样本相互关系,每对时间序列之间的连续时间滞后。令[公式:见文]表示用于估计这些相关矩阵的连续观测窗口的总数。我们分析了[公式:见文]而[公式:见文],[公式:见文]的渐近状态。在这些渐近条件下,研究了该块相关矩阵的特征值的线性统计性质,并证明了经验特征值分布收敛于Marcenko-Pastur分布。我们的结果对于解决测试大量时间序列是否不相关的问题是潜在的有用的。
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来源期刊
Random Matrices-Theory and Applications
Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty
CiteScore
1.90
自引率
11.10%
发文量
29
期刊介绍: Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.
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