Consistent GMM Residuals-Based Tests of Functional Form

Abstract

This paper presents a consistent GMM residuals-based test of functional form for time series models. By relating two moments we deliver a vector moment condition in which at least one element must be non-zero if the model is mis-specified. The test will never fail to detect mis-specification of any form for large samples, and is asymptotically chi-squared under the null, allowing for fast and simple inference. A simulation study reveals randomly selecting the nuisance parameter leads to more power than supremum-tests, and can obtain empirical power nearly equivalent to the most powerful test for even relatively small n.

Keywords: consistent test; conditional moment test; nonlinear model; GMM