Kernel-based testing with skewed and heavy-tailed data: Evidence from a nonparametric test for heteroskedasticity

We examine the performance of a nonparametric kernel-based specification test in the presence of skewed and heavy-tailed regressors. We start by modifying the Zheng (2009) test for heteroskedasticity by removing the random denominator in the test statistic, a common source of distortion for such tests. Asymptotic equivalence of our test statistic is shown and Monte Carlo simulations are provided to assess the finite sample performance. With normally distributed errors, we find slight improvements using our modified test when the regressors are asymmetric or symmetric without heavy-tails. Trimming and using a smaller bandwidth also improves size for these distributions. When the errors are heavy-tailed, the results are more favorable to our test.