Forecasting Volatility Using Double Shrinkage Methods

Abstract

In this paper, we propose and evaluate a shrinkage based methodology that is designed to improve the accuracy of forecasts of daily integrated volatility. Our approach is based on a two-step shrinkage procedure designed to extract latent common volatility factors from a large dimensional and high-frequency asset returns dataset. In the first step, we apply either LASSO or elastic net shrinkage on estimated integrated volatilities, in order to select a subset of assets that are informative about our target asset. In the second step, we utilize (sparse) principal component analysis on the selected assets, in order to estimate a latent return factor. This new factor is in turn utilized to construct a latent volatility factor. Although we find limited in-sample fit improvement, relative to various benchmark models currently used in the literature, all of our proposed factor-augmented forecasting models result in substantial predictive gains, as measured by out-of-sample R squared, and via the application of predictive accuracy tests. In particular, forecasting gains are observed at individual firm, sector, and market levels. Additionally, our empirical findings suggest that the first step of our procedure, which utilizes shrinkage, plays a crucial role in the success of our method, and the second step of our procedure also relies on shrinkage (via the use of SPCA) for optimal predictive performance.

Keywords: Forecasting, Latent Common Volatility Factor, Dimension Reduction, Factoraugmented Regression, High-Frequency Data, High-Dimensional Data

JEL Classification: C22, C52, C53, C58