COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1522

A Simple Approach to the Parametric Estimation
of Potentially Nonstationary Diffusions

Federico M. Bandi
Graduate School of Business, University of Chicago
and
Peter C.B. Phillips
Cowles Foundation for Research in Economics, Yale University

June 2005

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.

Keywords: Diffusion, Drift, Local time, Parametric estimation, Semimartingale, Stochastic differential equation

JEL Classification: C14, C22