Nonparametric Estimation and Misspecification Testing of Diffusion Models

Abstract:     
A nonparametric kernel estimator of the drift (diffusion) term in a diffusion model are developed given a preliminary parametric estimator of the diffusion (drift) term. Under regularity conditions, rates of convergence and asymptotic normality of the nonparametric estimators are established. We develop mis-specification tests of parametric diffusion models based on the nonparametric estimators, and derive the asymptotic properties of the tests. We also propose a Markov Bootstrap method for the test statistics to improve on the finite-sample approximations. The finite sample properties of the estimators are examined in a simulation study.

Number of Pages in PDF File: 33

Keywords: Diffusion, fixed-time distance asymptotics, kernel estimation, misspecification test, nonparametric

JEL Classification: C14, C22

working papers series