# 13-025/III (2013-01-31)

Manabu Asai, Soka University, Japan, and University of Pennsylvania; Michael McAleer, Erasmus School of Economics, Kyoto University, Japan, and Complutense University of Madrid, Spain
Diffusion process; Multivariate stochastic volatility; Long memory; Fractional Brownian motion, Generalized method of moments
JEL codes:
C32, C51, G13

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous timefractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the first step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in finite samples. The empirical results for the bivariate data of the S&P 500 and FTSE100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure.