Analyzing Commodity Futures Using Factor State-Space Models with Wishart Stochastic Volatility

Abstract

A factor state-space approach with stochastic volatility is proposed for modeling and forecasting the maturity structure of future commodity contracts. The proposed approach builds upon the dynamic 3-factor Nelson-Siegel model and its 4-factor Svensson extension and assumes for the latent level, slope and curvature factors a Gaussian vector autoregression with a multivariate Wishart stochastic volatility process. A computationally fast and easy to implement MCMC algorithm for the Bayesian posterior analysis is developed, which exploits the conjugacy of the Wishart and the Gaussian distribution. An empirical application to daily prices for contracts on crude oil with stipulated delivery dates ranging from one to 24 months ahead show that the estimated 4-factor Svensson model with two curvature factors provides a good parsimonious representation of the serial correlation in the individual prices and their volatility. It also shows that this model has a good out-of-sample forecast performance.