# Efficient Bayesian inference for multivariate factor stochastic volatility models with leverage

## TL;DR

This paper introduces an efficient Bayesian estimation method for multivariate factor stochastic volatility models with leverage, leveraging Particle Markov chain Monte Carlo techniques without mixture approximations.

## Contribution

It proposes a novel PMCMC-based sampling scheme for Factor MSV models that improves convergence and avoids mixture distribution approximations, enhancing Bayesian inference.

## Key findings

- Method successfully applied to simulated data
- Effective on daily US stock returns
- Improves convergence over previous methods

## Abstract

This paper discusses the efficient Bayesian estimation of a multivariate factor stochastic volatility (Factor MSV) model with leverage. We propose a novel approach to construct the sampling schemes that converges to the posterior distribution of the latent volatilities and the parameters of interest of the Factor MSV model based on recent advances in Particle Markov chain Monte Carlo (PMCMC). As opposed to the approach of Chib et al. (2006} and Omori et al. (2007}, our approach does not require approximating the joint distribution of outcome and volatility innovations by a mixture of bivariate normal distributions. To sample the free elements of the loading matrix we employ the interweaving method used in Kastner et al. (2017} in the Particle Metropolis within Gibbs (PMwG) step. The proposed method is illustrated empirically using a simulated dataset and a sample of daily US stock returns.