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REWEIGHTED FUNCTIONAL ESTIMATION OFDIFFUSION 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 estimatingnonparametric continuous-time diffusion models, butit may produce negative results for the diffusion(or volatility) functions and thus lead toinsensible inference. We demonstrate this using U.S.interest rate data. We propose a new functionalestimation method of the diffusion coefficient basedon reweighting the conventional Nadaraya–Watsonestimator. It preserves the appealing biasproperties of the local linear estimator and isguaranteed to be nonnegative in finite samples. Alimit theory is developed under mild requirements(recurrence) of the data generating mechanismwithout assuming stationarity or ergodicity.

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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 theco-editor Oliver B. Linton, two anonymousreferees, Donald W.K. Andrews, Zongwu Cai,Xiaohong Chen, Yuichi Kitamura, Taisuke Otsu,Peter C.B. Phillips, and other participants at theeconometrics seminar at Yale University and theNBER-NSF time series conference at Montreal.Special thanks go to Peter C.B. Phillips for hisguidance and encouragement. The author alsogratefully acknowledges the partial financialsupport provided by the University of AlbertaSchool of Business through the H.E. Pearsonfaculty award.

References

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