  We introduce a novel covariance estimator that exploits the heteroscedastic
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.
