Post by Sapphire Capital on Jul 11, 2008 6:57:42 GMT 4
Tilted Nonparametric Estimation of Volatility
Functions, 2nd Version
KE-LI XU
University of Alberta - School of Business
PETER C.B. PHILLIPS
Yale University - Cowles Foundation; University of Auckland; University of York (UK)
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April 13, 2008
Abstract:
This paper proposes a novel positive nonparametric estimator of the volatility function without relying on logarithmic or other transformations. The basic idea is to apply the re-weighted Nadaraya-Watson estimator of Hall and Presnell (1999, Journal of the Royal Statistical Society B) to squared mean regression residuals. The new volatility estimator is asymptotically equivalent to the local linear estimator and is restricted to be positive in finite samples. We also show its adaptiveness to the unknown mean function. Simulations are conducted to compare with other existing estimators and empirical applications including a jump diffusion model are provided to illustrate the usefulness of the proposed method.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1121244_code580609.pdf?abstractid=1121244&mirid=1
Functions, 2nd Version
KE-LI XU
University of Alberta - School of Business
PETER C.B. PHILLIPS
Yale University - Cowles Foundation; University of Auckland; University of York (UK)
--------------------------------------------------------------------------------
April 13, 2008
Abstract:
This paper proposes a novel positive nonparametric estimator of the volatility function without relying on logarithmic or other transformations. The basic idea is to apply the re-weighted Nadaraya-Watson estimator of Hall and Presnell (1999, Journal of the Royal Statistical Society B) to squared mean regression residuals. The new volatility estimator is asymptotically equivalent to the local linear estimator and is restricted to be positive in finite samples. We also show its adaptiveness to the unknown mean function. Simulations are conducted to compare with other existing estimators and empirical applications including a jump diffusion model are provided to illustrate the usefulness of the proposed method.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1121244_code580609.pdf?abstractid=1121244&mirid=1