Multivariate Levy Processes for Financial Returns

Abstract

We apply a signal processing technique known as independent component analysis (ICA) to multivariate financial time series. The main idea of ICA is to decompose the observed time series into statistically independent components (ICs). We further assume that the ICs follow the variance gamma (VG) process. The VG process is evaluated by Brownian motion with drift at a random time given by a gamma process. We build a multivariate VG portfolio model and analyze empirical results of the investment.