Predicting Daily Probability Distributions of S&P500 Returns
31 Pages Posted: 23 Oct 2008
Date Written: August 1998
Abstract
Most 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. Itis expressed as a mixture model: the dynamics of the individual states is modeled with so-called"experts" (potentially nonlinear neural networks), and the dynamics between the states is modeledusing a hidden Markov approach. The full density predictions are obtained by a weighted superpositionof 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 doesnot improve over simpler models, evaluating the prediction of the full density shows a clear out-of-sampleimprovement both over a simple GARCH(1,l) model (which assumes Gaussian distributedreturns) and over a "gated experts" model (which expresses the weighting for each state non-recursivelyas a function of external inputs). Several interpretations are given: the blending ofsupervised 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.
Keywords: Forecasting, Density Prediction, Conditional Distribution, Mixture Models, Time Series Analysis, Hidden Markov Models, Gated Experts, Hidden Markov Experts, Model Comparison, Density Evaluation, Computational Finance, Risk Management
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
A First Application of Independent Component Analysis to Extracting Structure from Stock Returns
By Andrew D. Back and Andreas Weigend
-
Modeling Volatility Using State Space Models
By Jens Timmer and Andreas Weigend
-
A Bootstrap Evaluation of the Effect of Data Splitting on Financial Time Series
By Blake Lebaron and Andreas Weigend