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 estimating
volatility and conditional covariances (given the past) for very
high-dimensional financial time series of asset price returns. FGD is a kind of
hybrid of nonparametric statistical function estimation and numerical
optimization. Our FGD algorithm is computationally feasible in multivariate
problems with dozens up to thousands of individual return
series. Moreover, we demonstrate on some synthetic and real data-sets
with dimensions up to 100, that it yields significantly, much
better predictions than more classical approaches such as a constant
conditional correlation GARCH-type model. Since our FGD algorithm is
constructed from a generic algorithm, the technique can be easily adapted
to other problems of learning in very high dimensions.
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