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A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

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Abstract

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1522.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1522.

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Length: 49 pages
Date of creation: Jun 2005
Date of revision:
Publication status: Published in Journal of Econometrics (April 2007), 137(2): 354-395
Handle: RePEc:cwl:cwldpp:1522

Note: CFP 1205.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Diffusion; Drift; Local time; Parametric estimation; Semimartingale; Stochastic differential equation;

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