Super-Consistent Tests of Lp-Functional Form

This paper develops a consistent test of best Lp-predictor functional form for a time series process. By functionally relating two moment conditions with different nuisance parameters we are able to construct a vector moment condition in which at least one element must be non-zero under the alternative. Specifically, we provide a sufficient condition for moment conditions of the type characterized by Stinchcombe and White (1998) to reveal model mis-specification for any nuisance parameter value. When the sufficient condition fails an alternative moment condition is guaranteed to work. A simulation study clearly demonstrates the superiority of a randomized test: randonly selecting the nuisance parameter leads to more power than average- and supremum-test functionals, and obtains empirical power nearly equivelant to uniformly most powerful tests in most cases.