COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1612

Tilted Nonparametric Estimation of Volatility Functions

Peter C.B. Phillips and Ke-Li Xu

June 2007

This paper proposes a novel positive nonparametric estimator of the conditional variance function without relying on a logarithmic transformation. The basic idea is to apply the re-weighted Nadaraya-Watson regression estimator of Hall and Presnell (1999, Journal of the Royal Statistical Society B, 61, 143--158) to squared residuals. The new conditional variance estimator is asymptotically equivalent to the local linear estimator and is restricted to be positive in finite samples. A small simulation is performed to compare the new methodology with Ziegelmann's (2002) local exponential and Yu and Jones's (2004) local likelihood-based estimators of the conditional variance.

Keywords: Conditional variance function; Empirical likelihood; Heteroskedasticity; Local linear estimator; Nadaraya-Watson estimator; Nonlinear time series; Nonparametric regression; Volatility

JEL Classification: C22