Testing Serial Correlation in Single Index Models

Abstract

In this article, we propose two testing procedures for the serial correlation in single index models by virtue of B spline approximation for unknown single index function. Under some regular conditions, we show that our proposed statistics asymptotically follow normal and χ² distribution. Many numerical studies illustrate that the proposed procedures can perform very well for moderate sample size.

Keywords:

• B spline
• Empirical likelihood
• Serial correlation
• Single index model

Mathematics Subject Classification:

• 62M10
• 62H12