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.