Bayesian Inference for Dynamic Cointegration Models with Application to Soybean Crush Spread

Abstract

Abstract In crush spread commodity trading strategies it is a common practice to select portfolio positions not based on statistical properties, but instead based on physical refinery conditions and efficiency in extracting byproducts from crushing raw soybeans to get soymeal and soyoil. The selected portfolio positions based on knowledge of refinery efficiency are then used to provide a basis for constructing the so called spread series, which is investigated separately using a model with a linear Gaussian structure. In this paper we take a statistical approach instead based on forming portfolio positions following from the cointegration vector relationships in the price series, which we argue endogenously take into consideration the respective demand and supply equilibrium dynamic associated to each component of the soybean complex spread. We propose an extension of the standard Cointegrated Vector Autoregressive Model that allows for a hidden linear trend under an error correction representation. The aim of this paper is to perform Bayesian estimation of the optimal cointegration vectors jointly with latent trends and to this end we develop an efficient Markov Chain Monte Carlo (MCMC) algorithm. The performance of this method is illustrated using numerical examples with simulated observations. Finally, we use the proposed model and MCMC sampler to perform analysis for soybean crush data. We will find the evidence in favour of the model structure proposed and present empirical justification that cointegration portfolio selection based on physical features of soybean market is sensitive to different roll adjustment methods used in the industry.