Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach

25 Pages Posted: 1 Mar 2021

See all articles by Vincent Tan

Vincent Tan

University of Oxford - Oxford-Man Institute of Quantitative Finance

Stefan Zohren

University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: January 2021

Abstract

We introduce a novel covariance estimator that exploits the heteroskedastic nature of financial time series by employing exponential weighted moving averages and shrinking the in-sample eigenvalues through cross-validation. Our estimator is model-agnostic in that we make no assumptions on the distribution of the random entries of the matrix or structure of the covariance matrix. Additionally, we show how Random Matrix Theory can provide guidance for automatic tuning of the hyperparameter which characterizes the time scale for the dynamics of the estimator. By attenuating the noise from both the cross-sectional and time-series dimensions, we empirically demonstrate the superiority of our estimator over competing estimators that are based on exponentially-weighted and uniformly-weighted covariance matrices.

Keywords: High-dimensional statistics, cross-validation, nonlinear shrinkage, exponential weighted moving average, Random Matrix Theory, rotation equivariance

JEL Classification: C13, C58, G11

Suggested Citation

Tan, Vincent and Zohren, Stefan, Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach (January 2021). Available at SSRN: https://ssrn.com/abstract=3745692 or http://dx.doi.org/10.2139/ssrn.3745692

Vincent Tan (Contact Author)

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Stefan Zohren

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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