Fully Nonparametric Estimation of Scalar Diffusion Models

48 Pages Posted: 14 Oct 2001

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Peter C. B. Phillips

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

Date Written: September 2001

Abstract

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter. The asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens (that is, we implement both infill and long span asymptotics). We prove consistency and convergence to mixtures of normal laws, where the mixing variates depend on the chronological local time of the underlying process, that is the time spent by the process in the vicinity of a spatial point. The estimation method and asymptotic results apply to both stationary and nonstationary processes.

Keywords: Diffusion, Drift, Infill Asymptotics, Kernel Density, Local Time, Long Span Asymptotics, Martingale, Nonparametric Estimation, Semimartingale, Stochastic Differential Equation

JEL Classification: C14, C22

Suggested Citation

Bandi, Federico Maria and Phillips, Peter C. B., Fully Nonparametric Estimation of Scalar Diffusion Models (September 2001). Available at SSRN: https://ssrn.com/abstract=285770

Federico Maria Bandi (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Peter C. B. Phillips

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

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

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
314
Abstract Views
4,076
Rank
176,134
PlumX Metrics