The predictive accuracy of various econometrics models, including random walks, vector autoregressive and vector error-correction models, are investigated using daily futures prices of 4 commodities (the S&P500 index, treasury bonds, gold and crude oil).

A class of nonlinear processes which have a root that is not constant, but is stochastic, and varying around unity is introduced. Th eprocess can be stationary for some periods, and mildly explosive for others.

In this paper, the authors provide some asymptotic results for the J-type test on non-nested hypotheses proposed by Davidson and MacKinnon (1981), in the context of I(1) time series.