Fast estimation of multivariate stochastic volatility

TL;DR

This paper introduces a fast Bayesian method for estimating multivariate stochastic volatility using state space models, suitable for real-time forecasting and model selection.

Contribution

It proposes a novel multiplicative model with inverted Wishart and multivariate singular beta distributions for volatility evolution, enabling efficient sequential updates.

Findings

Method is computationally fast and suitable for online forecasting

Effective in model selection using multiple criteria

Successfully applied to exchange rate data

Abstract

In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is employed. Being computationally fast, the resulting estimation procedure is particularly suitable for on-line forecasting. Three performance measures are discussed in the context of model selection: the log-likelihood criterion, the mean of standardized one-step forecast errors, and sequential Bayes factors. Finally, the proposed methods are applied to a data set comprising eight exchange rates vis-a-vis the US dollar.