CIRJE-F-297 "Stochastic volatility with leverage: fast and efficient likelihood inference"
Author Name Omori, Yasuhiro, Siddhartha Chib, Neil Shephard, Jouchi Nakajima
Date August 2004
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Remarks Revised in April 2006, subsequently published in Journal of Econometrics, 140, 425-449, 2007.

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. (1998) method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).