Consistent Gmm Residuals-based Tests of Functional Form

This paper presents a consistent Generalized Method of Moments (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 nonzero if the model is misspecified. The test will never fail to detect misspecification 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.