Nonparametric sign prediction of high-dimensional correlation matrix coefficients

TL;DR

This paper presents a nonparametric method to predict sign changes in high-dimensional correlation matrices, leveraging three-by-three relationships inspired by social cohesion theory, with applications to financial data.

Contribution

It introduces a novel nonparametric approach for sign prediction in high-dimensional correlation matrices based on three-by-three relationships.

Findings

Correlation sign stability depends on three-by-three relationships.

Method applied successfully to US and Hong Kong equities data.

Structure of correlation matrices influences sign stability.

Abstract

We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on three-by-three relationships inspired by Heider social cohesion theory in this regime. We apply our method to US and Hong Kong equities historical data to illustrate how the structure of correlation matrices influences the stability of the sign of its coefficients.