Semiparametric Specification Testing

We propose a specification test of a parametrically specified model against a weakly specified alternative. The latter is estimated using K nonparametric nearest neighbors (K-NN) in the context of an artificial regression. We derived the asymptotic distribution under the null hypothesis and under a series of local alternatives. Monte Carlo simulations suggest that the test is quite powerful although it has a tendency to over-reject under the null hypothesis.