Robust tests for ARCH in the presence of a misspecified conditional mean: A comparison of nonparametric approaches

This study compares the size and power of autoregressive conditional heteroskedasticity (ARCH) tests that are robust to the presence of a misspecified conditional mean. The approaches employed are based on two nonparametric regressions for the conditional mean: an ARCH test with a Nadaraya-Watson kernel regression and an ARCH test using a polynomial approximation regression. The two approaches do not require the specification of a conditional mean and can adapt to various nonlinear models, which are unknown a priori. The results reveal that the ARCH tests are robust to the misspecfied conditional mean models. The simulation results show that the ARCH tests based on the polynomial approximation regression approach have better properties of the size and power than those using the Nadaraya-Watson kernel regression approach for various nonlinear models.