Simple Robust Testing of Hypotheses in Nonlinear Models

Abstract

We develop test statistics to test hypotheses in nonlinear weighted regression models with serial correlation or conditional heteroscedasticity of unknown form. The novel aspect is that these tests are simple and do not require the use of heteroscedasticity autocorrelationconsistent (HAC) covariance matrix estimators. This new class of tests uses stochastic transformations to eliminate nuisance parameters as a substitute for consistently estimating 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 simple model and apply the new method of testing to an empirical example and illustrate that the size of the new test is less distorted than tests using HAC covariance matrix estimators.

KEY WORDS:

• Autocorrelation
• HAC estimator
• Inference
• Kernel
• Truncation log
• Variance estimation