The Journal of futures markets vol:28 issue:11 pages:1040-1065
The martingale hypothesis for futures prices is investigated using a nonparametric approach where it is assumed that the expected futures returns depend nonparametrically) on a linear combination of predictors. We first collapse the predictors into a single-index variable where the weights are identified up to scale, using the average derivative estimator proposed by Stoker
(1986). We then use the Nadaraya-Watson kernel estimator to calculate (and visually depict) the relation between the estimated index and the expected futures returns. An application to four agricultural commodity futures illustrates the technique. Out-of-sample results indicate
that for soybeans, wheat, and oats, the estimated index contains statistically significant information regarding the expected futures returns. We discuss implications of this finding for a non-infinitely risk-averse hedger.