Tilted Nonparametric Estimation of Volatility Functions with Empirical Applications

32 Pages Posted: 14 Jun 2007 Last revised: 19 Jul 2010

See all articles by Peter C. B. Phillips

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Ke-Li Xu

Indiana University Bloomington

Date Written: July 19, 2010

Abstract

This paper proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local level nonparametric regression applied to squared mean regression residuals. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be non-negative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite sample performance of the estimator. Two empirical applications are reported. One uses cross section data and studies the relationship between occupational prestige and income. The other uses time series data on Treasury bill rates to fit the total volatility function in a continuous-time jump diffusion model.

Keywords: Conditional variance function, Empirical likelihood, Conditional heteroskedasticity, Jump diffusion, Local linear estimator, Heteroskedastic nonparametric regression, Volatility

JEL Classification: C13, C14, C22

Suggested Citation

Phillips, Peter C. B. and Xu, Ke-Li, Tilted Nonparametric Estimation of Volatility Functions with Empirical Applications (July 19, 2010). Cowles Foundation Discussion Paper No. 1612, Available at SSRN: https://ssrn.com/abstract=993812

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

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Ke-Li Xu

Indiana University Bloomington ( email )

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