A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

50 Pages Posted: 18 Jul 2005

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

Date Written: June 2005

Abstract

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

Suggested Citation

Bandi, Federico Maria and Phillips, Peter C. B., A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions (June 2005). Cowles Foundation Discussion Paper No. 1522. Available at SSRN: https://ssrn.com/abstract=757347

Federico Maria Bandi

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Peter C. B. Phillips (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

University of Auckland ( email )

Private Bag 92019
Com. A room: 102
Auckland
New Zealand
+64 9 373 7599 x7596 (Phone)

University of Southampton

Southampton, SO17 1BJ
United Kingdom

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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