A fractionally integrated Wishart stochastic volatility model

ABSTRACT

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process, and derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. A two-step procedure is used, namely estimating the parameter of fractional integration via the local Whittle estimator 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 show a reasonable performance in finite samples. The empirical results for the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV process rather than the one-factor and two-factor models of the Wishart autoregressive process for the covariance structure.

KEYWORDS:

• Diffusion process
• fractional Brownian motion
• generalized method of moments
• long memory
• multivariate stochastic volatility

JEL Classification:

• C32
• C51
• G13

Acknowledgements

The authors are most grateful to Yoshi Baba, Karen Lewis, and Christian Hafner, three anonymous referees, and the editor, Esfandiar Maasoumi, for very helpful comments and suggestions.