Volatility Estimation with Functional Gradient Descent for Very High-Dimensional Financial Time Series

Francesco Audrino and Peter Bühlmann

August 2001

Abstract: We propose a functional gradient descent algorithm (FGD) for estimatingvolatility and conditional covariances (given the past) for veryhigh-dimensional financial time series of asset price returns. FGD is a kind ofhybrid of nonparametric statistical function estimation and numericaloptimization. Our FGD algorithm is computationally feasible in multivariateproblems with dozens up to thousands of individual returnseries. Moreover, we demonstrate on some synthetic and real data-sets with dimensions up to 100, that it yields significantly, muchbetter predictions than more classical approaches such as a constantconditional correlation GARCH-type model. Since our FGD algorithm isconstructed from a generic algorithm, the technique can be easily adaptedto other problems of learning in very high dimensions.

Download: Compressed Postscript (181 Kb).