Bayesian Cointegration with Linear State Space Models: a case study on the Soybean Crush Spread

In this paper we investigate how vector autoregressive (VAR) models can
be used to study the soybean crush spread. By crush spread we mean a time series marking the difference between a weighted combination of the value of soymeal and soyoil to the value of the original soybeans. Commodity industry practitioners often use fixed prescribed values for these weights, which do not take into account any time varying effects or any financial market based dynamic features that can be discerned from futures price data. In this work we address this issue by proposing an appropriate time series model with cointegration. Our model consists of an extension of a particular VAR model used widely in econometrics. Our extensions are inspired by the problem at hand and allow for a time varying covariance structure and a time varying intercept to account for seasonality. To perform Bayesian inference we design an efficient Markov Chain Monte Carlo algorithm, which is based on the approach of Koop et al. [2009]. Our investigations on prices obtained from futures contracts data confirmed that the added features in our model are useful in reliable statistical determination
of the crush spread. Although the interest here is on the soybean crush spread, our approach is applicable also to other tradable spreads such as oil and
energy based crack or spark.