HIDDEN MARKOV EXPERTS

Andreas S. Weigend and Shanming Shi
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Andreas S. Weigend: ShockMarket Corporation, 151 Lytton Avenue, Palo Alto, CA 94301, USA
Shanming Shi: J. P. Morgan & Co. Inc., 60 Wall Street, New York, NY 10260, USA

Chapter 2 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 35-70 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractMost approaches in forecasting merely try to predict the next value of the time series. In contrast, this paper presents a framework to predict the full probability distribution. It is expressed as a mixture model: the dynamics of the individual states is modeled with so-called "experts" (potentially non-linear neural networks), and the dynamics between the states is modeled using a hidden Markov approach. The full density predictions are obtained by a weighted superposition of the individual densities of each expert. This model class is called "hidden Markov experts".Results are presented for daily S&P500 data. While the predictive accuracy of the mean does not improve over simpler models, evaluating the prediction of the full density shows a clear out-of-sample improvement both over a simple GARCH(1,1) model (which assumes Gaussian distributed returns) and over a "gated experts" model (which expresses the weighting for each state non-recursively as a function of external inputs). Several interpretations are given: the blending of supervised and unsupervised learning, the discovery of hidden states, the combination of forecasts, the specialization of experts, the removal of outliers, and the persistence of volatility.

Date: 2001
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