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Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models

39 Pages Posted: 22 Mar 2010  

Dennis Kristensen

University College London; University of Aarhus - CREATES; Cemmap (Centre for Microdata Methods and Practice)

Date Written: March 15, 2010


We propose novel misspecification tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in Kristensen (Journal of Econometrics, 2010). We first demonstrate that given a preliminary estimator of either the drift or the diffusion term in a diffusion model, nonparametric kernel estimators of the remaining term can be obtained. We then propose misspecification tests of semparametric and fully parametric diffusion models that compare estimators of the transition density under the relevant null and alternative. The asymptotic distribution of the estimators and tests under the null are derived, and the power properties are analyzed by considering contiguous alternatives. Test directly comparing the drift and diffusion estimators under the relevant null and alternative are also analyzed. Markov Bootstrap versions of the test statistics are proposed to improve on the finite-sample approximations. The finite sample properties of the estimators are examined in a simulation study.

Keywords: diffusion process, kernel estimation, nonparametric, specification testing, semiparametric, transition density

JEL Classification: C12, C13, C14, C22

Suggested Citation

Kristensen, Dennis, Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models (March 15, 2010). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 10-10. Available at SSRN: or

Dennis Kristensen (Contact Author)

University College London ( email )

Gower Street
London WC1E 6BT, WC1E 6BT
United Kingdom
+44 (0)20 7679 5846 (Phone)


University of Aarhus - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C

Cemmap (Centre for Microdata Methods and Practice) ( email )

7 Ridgmount Street
London WC1E 7AE, WC1E 7 AE
United Kingdom

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