This article contributes to the debate on time series properties of commodity cash and futures markets and the impact of speculation on commodity futures markets. We reconcile production theory, which predicts cash commodity prices will be mean-reverting, with the efficient market hypothesis which is consistent with unit root process for futures prices. It is shown that when the underlying cash price series does not contain a unit root, a nearby futures price series can be nonlinear, having martingale properties within each contract segment, and mean-reverting changes at contract rollover points. We develop a novel ECM-BEKK-MEX model that handles nonlinearities in futures prices in a simple and practical way, and allows full flexibility in modeling the impact of speculation on conditional cash and futures price variances while preserving positive definiteness of the bivariate variance matrix. The model is applied to the U.S. dairy sector.