# Eigenvalue and Eigenvector Statistics in Time Series Analysis

## TL;DR

This paper develops a supersymmetric theoretical framework to analyze the eigenvalue and eigenvector statistics of cross-correlation matrices in correlated time series, providing a universal benchmark for complex system analysis.

## Contribution

It introduces a novel supersymmetric approach to derive analytical results for eigenvector statistics in correlated time series, filling a gap in existing theoretical understanding.

## Key findings

- Analytical expressions for eigenvector statistics derived
- Benchmark results for correlated signal analysis established
- Framework applicable to diverse complex systems

## 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.