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REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS

Published online by Cambridge University Press:  30 September 2009

Ke-Li Xu
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Abstract

The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 541 - 563
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The author has benefited from comments by the co-editor Oliver B. Linton, two anonymous referees, Donald W.K. Andrews, Zongwu Cai, Xiaohong Chen, Yuichi Kitamura, Taisuke Otsu, Peter C.B. Phillips, and other participants at the econometrics seminar at Yale University and the NBER-NSF time series conference at Montreal. Special thanks go to Peter C.B. Phillips for his guidance and encouragement. The author also gratefully acknowledges the partial financial support provided by the University of Alberta School of Business through the H.E. Pearson faculty award.

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