Generalized Self-Organizing Mixture Autoregressive Model for Modeling Financial Time Series

Abstract

The mixture autoregressive (MAR) model regards a time series as a mixture of linear regressive processes. A self-organizing algorithm has been used together with the LMS algorithm for learning the parameters of the MAR model. The self-organizing map has been used to simplify the mixture as a winner-takes-all selection of local models, combined with an autocorrelation coefficient based measure as the similarity measure for identifying correct local models and has been shown previously being able to uncover underlying autoregressive processes from a mixture. In this paper the self-organizing network is further generalized so that it fully considers the mixing mechanism and individual model variances in modeling and prediction of time series. Experiments on both benchmark time series and several financial time series are presented. The results demonstrate the superiority of the proposed method over other time-series modeling techniques on a range of performance measures including mean-square-error, prediction rate and accumulated profits.