Computationally Efficient Estimation of Factor Multivariate Stochastic Volatility Models

An Markov chain Monte Carlo simulation method based on a two stage de-layed rejection Metropolis-Hastings algorithm is proposed to estimate a factor multivariate stochastic volatility model. The first stage uses ‘k-step iteration’ towards the mode, with k small, and the second stage uses an adaptive random walk proposal density. The marginal likelihood approach of Chib (1995) is used to choose the number of factors, with the posterior density ordinates approxi-mated by Gaussian copula. Simulation and real data applications suggest that the proposed simulation method is computationally much more efficient than the approach of Chib, Nardari, and Shephard (2006). This increase in computational efficiency is particularly important in calculating marginal likelihoods because it is necessary to carry out the simulation a number of times to estimate the pos-terior ordinates for a given marginal likelihood. In addition to the Markov chain Monte Carlo method, the paper also proposes a fast approximate EM method to estimate the factor multivariate stochastic volatility. The estimates from the approximate EM method are of interest in their own right but are especially use-ful as initial inputs to Markov chain Monte Carlo methods, making them more efficient computationally. The methodology is illustrated using simulated and real examples