Detecting changes in covariance via random matrix theory

TL;DR

This paper introduces a new non-linear test statistic based on Random Matrix Theory for detecting changes in the covariance structure of moderate dimensional time series, independent of the covariance matrix's underlying structure.

Contribution

It proposes a novel, structure-independent test statistic and demonstrates its convergence to a normal distribution, outperforming existing methods in simulations and a real-world application.

Findings

Test statistic converges to a normal distribution under null hypothesis

Outperforms existing methods in simulated datasets

Successfully applied to soil surface water change detection

Abstract

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying structure of the covariance matrix. We discuss how results from Random Matrix Theory, can be used to study the behaviour of our test statistic in a moderate dimensional setting (i.e. the number of variables is comparable to the length of the data). In particular, we demonstrate that the test statistic converges point wise to a normal distribution under the null hypothesis. We evaluate the performance of the proposed approach on a range of simulated datasets and find that it outperforms a range of alternative recently proposed methods. Finally, we use our approach to study changes in the amount of water on the surface of a plot of soil which feeds into model development for degradation of surface piping.