Multivariate stochastic volatility with Bayesian dynamic linear models

TL;DR

This paper introduces a Bayesian method for estimating and forecasting multivariate volatility using matrix-variate dynamic linear models with stochastic evolution, applied to metal prices, offering a flexible and effective approach.

Contribution

It develops a novel Bayesian framework employing Wishart and multivariate beta distributions for multivariate volatility estimation with a flexible variance modeling approach.

Findings

Effective application to metal price data

Overcomes limitations of existing volatility models

Provides a flexible, pragmatic variance modeling method

Abstract

This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed estimation theory is applied to a four-dimensional time series, comprising spot prices of aluminium, copper, lead and zinc of the London metal exchange. The empirical findings suggest that the proposed Bayesian procedure can be effectively applied to financial data, overcoming many of the disadvantages of existing volatility models.