A NONPARAMETRIC GOODNESS-OF-FIT-BASED TEST FOR CONDITIONAL HETEROSKEDASTICITY

In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit (R²) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being appropriately standardized, the nonparametric R² is asymptotically normally distributed under the null hypothesis and a sequence of Pitman local alternatives. We also prove the consistency of the test and propose a bootstrap method to obtain the bootstrap <italic>p</italic>-values. We conduct a small set of simulations and compare our test with some popular parametric and nonparametric tests in the literature.