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A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model

Published online by Cambridge University Press:  11 February 2009

George J. Jiang  and
John L. Knight
George J. Jiang
Affiliation:
University of Groningen
John L. Knight
Affiliation:
University of Western Ontario
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Abstract

In this paper, we propose a nonparametric identification and estimation procedure for an ltd diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this paper deals with general ltd diffusion processes and avoids any functional form specification for either the drift function or the diffusion function. It is shown that under certain regularity conditions the nonparametric diffusion function estimator is pointwise consistent and asymptotically follows a normal mixture distribution. Under stronger conditions, a consistent nonparametric estimator of the drift function is also derived based on the diffusion function estimator and the marginal density of the process. An application of the nonparametric technique to a short-term interest rate model involving Canadian daily 3-month treasury bill rates is also undertaken. The estimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion functions.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 5 , October 1997 , pp. 615 - 645
Copyright
Copyright © Cambridge University Press 1997

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