Matrix-State Particle Filter for Wishart Stochastic Volatility Processes

Abstract

This work deals with multivariate stochastic volatility models, which account for a time-varying variance-covariance structure of the observable variables. We focus on a special class of models recently proposed in the literature and assume that the covariance matrix is a latent variable which follows an autoregressive Wishart process. We review two alternative stochastic representations of the Wishart process and propose Markov-Switching Wishart processes to capture different regimes in the volatility level. We apply a full Bayesian inference approach, which relies upon Sequential Monte Carlo (SMC) for matrix-valued distributions and allows us to sequentially estimate both the parameters and the latent variables.

Keywords: Multivariate Stochastic Volatility, Matrix-State Particle Filters, Sequential Monte Carlo, Wishart Processes, Markov Switching

JEL Classification: C11, C15, C32