Can oil prices help estimate commodity futures prices? The cases of copper and silver

There is an extensive literature on modeling the stochastic process of commodity futures. It has been shown that models with several risk factors are able to adequately fit both the level and the volatility structure of observed transactions with reasonable low errors. One of the characteristics of commodity futures markets is the relatively short term maturity of their contracts, typically ranging for only a few years. This poses a problem for valuing long term investments that require extrapolating the observed term structure. There has been little work on how to effectively do this extrapolation and in measuring its errors. (Cortazar et al., 2008a) and (Cortazar et al., 2008b) propose a multicommodity model that jointly estimates two commodities, one with much longer maturity futures contracts than the other, showing that futures prices of one commodity may be useful information for estimating the stochastic process of another. They implement the procedure using highly correlated commodities like WTI and Brent. In this paper we analyze using prices of long term oil futures contracts to help estimate long term copper and silver future prices. We start by analyzing the performance of the (Cortazar et al., 2008a) and (Cortazar et al., 2008b) multicommodity model, now applied to oil-copper and oil-silver which have much lower correlation than the WTI-Brent contracts. We show that for these commodities with lower correlation the multicommodity model seems not to be effective. We then propose a modified multicommodity model with a much simpler structure which is easier to estimate and that uses the non-stationary long term process of oil to help estimate long term copper and silver futures prices, achieving a much better fit than using available individual or multicommodity models.