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.

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.