  This study compares statistical properties of ARCH tests that are robust to
the presence of the misspecified conditional mean. The approaches employed in
this study are based on two nonparametric regressions for the conditional mean.
First is the ARCH test using Nadayara-Watson kernel regression. Second is the
ARCH test using the polynomial approximation regression. The two approaches do
not require specification of the conditional mean and can adapt to various
nonlinear models, which are unknown a priori. Accordingly, they are robust to
misspecified conditional mean models. Simulation results show that ARCH tests
based on the polynomial approximation regression approach have better
statistical properties than ARCH tests using Nadayara-Watson kernel regression
approach for various nonlinear models.
