Cleaning the covariance matrix of strongly nonstationary systems with time-independent eigenvalues

TL;DR

This paper introduces a novel data-driven method for reducing noise in covariance matrices of nonstationary systems by using input-independent eigenvalues that capture long-term influences, outperforming traditional stationary methods.

Contribution

The paper presents a new approach to covariance matrix denoising in nonstationary systems using input-independent eigenvalues, improving over existing stationary-based methods.

Findings

Outperforms traditional stationary methods in nonstationary settings

Effective in financial portfolio variance minimization

Works well with both real and synthetic data

Abstract

We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues that are highly dependent on the inputs, as common sense would suggest. Our approach proposes instead to use a set of eigenvalues totally independent from the inputs and that encode the long-term averaging of the influence of the future on present eigenvalues. Such an influence can be the predominant factor in nonstationary systems. Using real and synthetic data, we show that our data-driven method outperforms optimal methods designed for stationary systems for the filtering of both covariance matrix and its inverse, as illustrated by financial portfolio variance minimization, which makes out method generically relevant to many problems of multivariate inference.