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Estimation in two classes of semiparametric diffusion models

Kristensen, Dennis (2004) Estimation in two classes of semiparametric diffusion models. Discussion paper, 500. Financial Markets Group, London School of Economics and Political Science, London, UK.

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Abstract

In this paper we propose an estimation method for two classes of semiparametric scalar diffusion models driven by a Brownian motion: In the first class, only the diffusion term is parameterised while the drift is unspecified; in the second, the drift term is specified while the diffusion term is of unknown form. The estimation method is based on the assumption of stationarity of the observed process. This allows us to express the unspecified term as a functional of the parametric part and the stationary density. A MLE-like estimator for the parametric part and a kernel estimator the nonparametric part are defined for a discrete sample with a fixed time distance between the observations. We show that the parametric part of the estimator is √n-consistent, while the nonparametric part has a slower convergence rate. Also, the asymptotic distribution of the estimator derived. We give a brief discussion of the issue of semiparametric efficiency, and present a small simulation study of the finite-sample performance of our estimator.

Item Type: Monograph (Discussion Paper)
Official URL: http://fmg.lse.ac.uk
Additional Information: © 2004 The Author
Library of Congress subject classification: H Social Sciences > HG Finance
H Social Sciences > HB Economic Theory
Sets: Research centres and groups > Financial Markets Group (FMG)
Collections > Economists Online
Collections > LSE Financial Markets Group (FMG) Working Papers
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: 500
Date Deposited: 06 Aug 2009 08:58
URL: http://eprints.lse.ac.uk/24739/

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