Testing Symmetry of the Error Distribution in Nonlinear Heteroscedastic Models

Abstract

Using the empirical characteristic function, we derive a Cramér-von Mises test for symmetry of the error distribution in a class of nonlinear parametric heteroscedastic models. We study the convergence of the residual-based empirical distribution function. We establish a functional limit theorem for an empirical process of residuals, and investigate the asymptotic null distribution function of our test statistic. A simulation experiment is conducted to evaluate small-sample performances of our test.

Keywords:

• Functional limit theorem
• Heteroscedastic models
• Symmetry
• Testing

Mathematics Subject Classification:

• 62M10
• 60F17
• 62G10