Simple robust testing of hypotheses in nonlinear models

We develop test statistics to test hypotheses in nonlinear weighted regress ion models with serial correlation or conditional heteroscedasticity of unk nown form. The novel aspect is that these tests are simple and do not requi re the use of heteroseedasticity autocorrelation-consistent (HAC) covarianc e matrix estimators. Th-is new class of tests uses stochastic transformatio ns to eliminate nuisance parameters as a substitute for consistently estima ting the nuisance parameters. We derive the limiting null distributions of these new tests in a general nonlinear setting, and show that although the tests have nonstandard distributions, the distributions depend only on the number of restrictions being tested. We perform some simulations on a simpl e model and apply the new method of testing to an empirical example and ill ustrate that the size of the new test is less distorted than tests using HA C covariance matrix estimators.