Identification of cross and autocorrelations in time series within an approach based on Wigner eigenspectrum of random matrices

TL;DR

This paper introduces a novel random matrix-based method utilizing Wigner eigenspectrum to differentiate between autocorrelations and cross correlations in time series, demonstrated on financial stock data.

Contribution

It presents an original approach that replaces Wishart eigenspectrum with Wigner eigenspectrum for analyzing correlations in time series.

Findings

Successfully distinguishes autocorrelations from cross correlations in financial data.

Provides a new tool for analyzing complex dependencies in multivariate time series.

Enhances understanding of correlation structures in stock market data.

Abstract

We present an original and novel method based on random matrix approach that enables to distinguish the respective role of temporal autocorrelations inside given time series and cross correlations between various time series. The proposed algorithm is based on properties of Wigner eigenspectrum of random matrices instead of commonly used Wishart eigenspectrum methodology. The proposed approach is then qualitatively and quantitatively applied to financial data in stocks building WIG (Warsaw Stock Exchange Index).