Semiparametric Specification Testing of Nonlinear Models

We propose a specification test of a parametrically specified nonlinear model against a weakly specified alternative. We generalize a similar test procedure proposed by Delgado and Stengos (1990) to test the specification of a linear model. We estimate the alternative model by using K nonparametric nearest neighbors (K-NN) in the context of an artificial regression. We derive the asymptotic distribution of the test statistic under the null hypothesis and under a series of local alternatives. Monte Carlo simulations suggest that the test has good power and size characteristics.