Computationally Efficient Estimation of Factor Multivariate Stochastic Volatility Models

TL;DR

This paper introduces a computationally efficient MCMC and EM-based approach for estimating factor multivariate stochastic volatility models, improving speed and accuracy in financial data analysis.

Contribution

It proposes a novel two-stage delayed rejection MCMC algorithm and an approximate EM method, enhancing estimation efficiency and providing practical initial values.

Findings

The MCMC method is significantly faster than previous approaches.

The EM method provides reliable initial estimates for MCMC.

Applications demonstrate improved computational performance on real and simulated data.

Abstract

An MCMC simulation method based on a two stage delayed rejection Metropolis-Hastings algorithm is proposed to estimate a factor multivariate stochastic volatility model. The first stage uses kstep 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 approximated 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 posterior ordinates for a given marginal likelihood. In addition to the MCMC method, the paper also proposes a fast approximate EM method to estimate the factor multivariate stochastic volatility model. The estimates from the approximate EM method are of interest in their own right, but are especially useful as initial inputs to MCMC methods, making them more efficient computationally. The methodology is illustrated using simulated and real examples.