Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models

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  • Dennis Kristensen
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 thediffusion 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.
Original languageEnglish
PublisherDepartment of Economics, University of Copenhagen
Number of pages22
Publication statusPublished - 2010

    Research areas

  • Faculty of Social Sciences - diffusion process, kernel estimation, nonparametric, specification testing, semiparametric, transition density

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