Fractional Gaussian noise criterion for correlations characterization: a random-matrix-theory inspired perspective

TL;DR

This paper presents a novel random-matrix-theory-based method to analyze autocorrelation matrices of time series, revealing correlation structures inaccessible to traditional autocorrelation analysis, with applications to stock markets and turbulence.

Contribution

It introduces a fractional Gaussian noise-based criterion for autocorrelation analysis using random matrix theory, providing a new quantitative tool for time series correlation characterization.

Findings

Stock market data aligns with fractional Gaussian noise despite non-Gaussian returns.

Turbulence data deviates from fractional Gaussian noise despite Gaussian velocity distribution.

The method uncovers hidden correlation structures beyond traditional autocorrelation analysis.

Abstract

We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the straight analysis of the autocorrelation function. Exploiting the well-studied hierarchy of the fractional Gaussian noise (fGn), an \emph{in situ} criterion for the sake of a quantitative comparison with the autocorrelation data is offered. We illustrate the applicability of our method by two paradigmatic examples from the orthodox context of the stock markets and the turbulence. Quite strikingly, a remarkable agreement with the fGn is achieved notwithstanding the non-Gaussianity in returns of the stock market. In the latter context, on the contrary, a significant deviation from an fGn is observed despite a Gaussian distribution of the velocity profile of the turbulence.