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

## TL;DR

This paper introduces a new method to detect signals in stock return correlations that standard techniques miss.

## Contribution

A stochastic field theory model is proposed to detect signals within the continuous eigenvalue spectrum of stock return correlations.

## Key findings

- A signal was detected in the largest eigenvalues of the stock return correlation matrix.
- Standard methods like PCA fail to detect signals in the continuous eigenvalue spectrum.
- The model was applied to S&P 500 stock data, revealing hidden correlations.

## 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.