Pre-Shrinkage: Improved Volatility Forecasting Using Biased Time-Series

Abstract

We propose to model and forecast realized covariances by estimating reduced form models on 'pre-shrunk' time-series. By adapting established linear and non-linear shrinkage techniques to high-frequency volatility estimates we construct an alternative time-series that is biased, but offers an expected Frobenius norm improvement with respect to the latent covariance matrix. Both parameter estimates and forecasts are based on the pre-shrunk series. We document statistically and economically significant forecast improvements based on statistical loss functions with respect to both the standard and shrunk realized covariance measures, for cross-sectional dimensions ranging from one to over a hundred. The forecasts also lead to improved global minimum variance portfolios, which do not inherently favour either series. The pre-shrunk models compare favourably to alternative measurement-error alleviating techniques.