Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity

Abstract

We study the efficient estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. The effect of weighting on nonparametric regressions is examined, and cases when efficiency gain can be achieved via weighting is investigated. We show that in many popular nonparametric regression models our method has lower asymptotic variance than the usual unweighted procedures. A Monte Carlo investigation is conducted and confirms the efficiency gain over conventional nonparametric regression estimators in finite samples. We use our method in several common applications concerning stock returns.

Keywords: GARCH; Kernel; Prediction

JEL Classification: C10, C13, C14