Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach
25 Pages Posted: 1 Mar 2021
Date Written: January 2021
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
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