A new analysis of VIX using mixture of regressions: Examination and short-term forecasting for the S & P 500 market

Abstract

A novel approach to the analysis of S & P 500 market fluctuations is proposed using a K-component mixture of regressions model. The Barndorff-Nielsen and Shephard stochastic model is employed where the estimates of jumps of log-returns are governed by Lévy subordinators. Daily VIX and VIX² close prices are analyzed as the indicators of log-return volatility and the corresponding variance of the S & P 500 index using the mixture model. The behavior of the S & P 500 market from 1 August 2005 to 31 December 2009 is analyzed and forecasted. A set of rules are provided to predict monthly fluctuation in the S & P 500 market. The procedure used in this paper gives a novel approach for constructing an “indicator”of non-Gaussian jump of an empirical data set in finance using mixture of regression (Gaussian) analysis.