Summary We investigate how vector auto‐regressive 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. We address this issue by proposing an appropriate time series model with cointegration. Our model consists of an extension of a particular vector auto‐regressive model that is 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 and his co‐workerss. 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 and spark spreads.

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Abstract. We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. Then we will propose extensions that can allow the ideas in both methods to be applied for cointegrated time series with non-Gaussian noise. We illustrate the efficiency and accuracy of these extensions using appropriate numerical experiments.

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