Empirical evidence for nonlinearity and irreversibility of commodity futures prices

Theory suggests that commodity futures price levels and returns data may exhibit both nonlinear and nonreversible features. This paper attempts to provide a thorough empiri- cally investigation of these claims. The data set is composed of 25 individual continuous contract commodity futures series which fall within a number of industry sectors including softs, precious metals, energy, and livestock. Employing both time-domain and frequency- domain tests examining the higher order cumulant properties of these series, it is shown that they exhibit both nonlinearities and irreversibility differing across industry sector. Furthermore, in modeling these series I estimate a number of parametric models able to capture irreversibility such as the linear mixed causal/noncausal autoregressive model and various purely causal nonlinear models, since there is a close connection between these two classes of models. It is shown that the linear causal ARMA model is unable to adequately account for the features of the data and while the mixed causal/noncausal model improves model fit significantly by capturing latent irreversibility, the vast majority of the nonlinearity these series exhibit is of the “nonlinear in variance” type. Finally, out of sample forecasts and an evaluation of the estimated unconditional distribution of the mixed causal/noncausal models suggest that there may still exist model misspecification.