Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility (SV) Models

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Gregor Kastner*+ and Sylvia Frühwirth-Schnatter and Hedibert Freitas Lopes
• Companies: WU Vienna University of Economics and Business and WU Vienna University of Economics and Business and The University of Chicago Booth School of Business
• Keywords: Markov Chain Monte Carlo (MCMC) ; State-Space Model ; Auxiliary Mixture Sampling ; Ancillarity-Sufficiency Interweaving Strategy (ASIS) ; Dynamic Covariance ; Exchange Rate Data

Abstract

Multivariate factor SV models are increasingly used for the analysis of multivariate financial and economic time series because they can capture the volatility dynamics by a small number of latent factors. The main advantage of such a model is its parsimony, where all variances and covariances of a time series vector are governed by a low-dimensional common factor with the components following independent SV models. For high dimensional problems of this kind, Bayesian MCMC estimation is a very efficient estimation method, however, it is associated with a considerable computational burden when the number of assets is moderate to large. To overcome this, we avoid the usual forward-filtering backward-sampling (FFBS) algorithm by sampling "all without a loop" (AWOL), consider various reparameterizations such as (partial) non-centering, and apply an ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation at an univariate level, which can be applied directly to heteroscedasticity estimation for latent variables such as factors. To show the effectiveness of our approach, we apply the model to a vector of daily exchange rate data.