Eigenvalue and Eigenvector Statistics in Time Series Analysis

Abstract

The study of correlated time-series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of complex systems. Despite this fact, no general result is known for the statistics of eigenvectors of the cross-correlations of correlated time-series. Here we use supersymmetric theory to provide novel analytical results that will serve as a benchmark for the study of correlated signals for a vast community of researchers.

8 pages, 3 figures

References in corpus (8)

• Anderson Transitions
• The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows
• Cleaning large correlation matrices: tools from random matrix theory
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices
• Eigenvalue Density of the Doubly Correlated Wishart Model: Exact Results
• Hyperbolic Hubbard-Stratonovich transformation made rigorous
• Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes

Cited by in corpus (4)

• The Physics of Financial Networks
• Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
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• A random matrix perspective of cultural structure: groups or redundancies?