Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity

75 Pages Posted: 26 May 2015 Last revised: 9 May 2016

See all articles by Oliver B. Linton

Oliver B. Linton

University of Cambridge

Zhijie Xiao

Boston College - Department of Finance and Department of Economics

Date Written: May 9, 2016

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

Suggested Citation

Linton, Oliver B. and Xiao, Zhijie, Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity (May 9, 2016). Available at SSRN: https://ssrn.com/abstract=2610020 or http://dx.doi.org/10.2139/ssrn.2610020

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Zhijie Xiao

Boston College - Department of Finance and Department of Economics ( email )

United States

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