Signal inference in financial stock return correlations through phase-ordering kinetics in the quenched regime

TL;DR

This paper introduces a stochastic field theory approach to detect signals in stock return correlation matrices, especially within the continuous eigenvalue spectrum where traditional methods like PCA fail, demonstrated on S&P 500 data.

Contribution

We develop a novel stochastic field theory model to identify signals in the eigenvalue spectrum of financial correlation matrices, extending detection capabilities beyond standard PCA limitations.

Findings

Detected signals in the largest eigenvalues within the continuous spectrum of S&P 500 correlations.

Established a new detection threshold for signals in the eigenvalue distribution.

Showed that traditional methods like PCA cannot detect these signals.

Abstract

Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock return correlation matrix typically aligns with a rescaled Marchenko-Pastur distribution, indicating no detectable signal. In this study, we introduce a stochastic field theory model to establish a detection threshold for signals present in the limit where the eigenvalues are within the continuous spectrum, which itself closely resembles that of a random matrix where standard methods such as principal component analysis fail to infer a signal. We then apply our method to Standard & Poor's 500 financial stocks' return correlations, detecting the presence of a signal in the largest eigenvalues within the continuous spectrum.