Measuring bias in a term-structure model of commodity prices through the comparison of simultaneous and sequential estimation

Abstract

This study examines bias in a term-structure model of commodity prices in specifying the true stochastic dynamics of underlying spot price. The bias is quantified by comparing the model estimated by the conventional method of estimating all model parameters simultaneously with a panel of futures prices and the model estimated by an alternative method of estimating model parameters in two steps. In this alternative approach, a subset of model parameters is first estimated on the first difference of observed futures prices so that these parameters are free from bias in specifying deterministic price variation and the dynamics of the underlying state variables. In the second step, the remaining model parameters are estimated on the futures price equations, while holding the parameters estimated in the first step. Empirical applications to four commodities (gold, crude oil, natural gas, and corn) reveal that the two-factor model widely considered in the literature is subject to a misspecification bias of substantial size. Out-of-sample forecast test indicates that, for three of the four commodities considered, the model estimated by the sequential method yields a considerably more accurate price forecast than the model estimated by the simultaneous method.