Dynamic modeling of commodity futures prices

Theory suggests that physical commodity prices may exhibit nonlinear features such as bubbles and various types of asymmetries. This paper investigates these claims empirically by introducing a new time series model apt to capture such features. The data set is composed of 25 individual, continuous contract, commodity futures price series, representative of a number of industry sectors including softs, precious metals, energy, and livestock. It is shown that the linear causal ARMA model with Gaussian innovations is unable to adequately account for the features of the data. In the purely descriptive time series literature, often a threshold autoregression (TAR) is employed to model cycles or asymmetries. Rather than take this approach, we suggest a novel process which is able to accommodate both bubbles and asymmetries in a flexible way. This process is composed of both causal and noncausal components and is formalized as the mixed causal/noncausal autoregressive model of order (r, s). Estimating the mixed causal/noncausal model with leptokurtic errors, by an approximated maximum likelihood method, results in dramatically improved model fit according to the Akaike information criterion. Comparisons of the estimated unconditional distributions of both the purely causal and mixed models also suggest that the mixed causal/noncausal model is more representative of the data according to the Kullback-Leibler measure. Moreover, these estimation results demonstrate that allowing for such leptokurtic errors permits identification of various types of asymmetries. Finally, a strategy for computing the multiple steps ahead forecast of the conditional distribution is discussed.