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Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models

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  • Dennis Kristensen

    (Department of Economics, University of Columbia, NY)

Abstract

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.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 10-10.

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Length: 17 pages
Date of creation: Mar 2010
Date of revision:
Handle: RePEc:kud:kuiedp:1010

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Related research

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

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Cited by:
  1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 22(3), pages 361-411, September.

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