TY - UNPB

T1 - Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models

AU - Kristensen, Dennis

N1 - JEL-classification: C12, C13, C14, C22

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Faculty of Social Sciences

KW - diffusion process

KW - kernel estimation

KW - nonparametric

KW - specification testing

KW - semiparametric

KW - transition density

M3 - Working paper

BT - Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models

PB - Department of Economics, University of Copenhagen

ER -