Physics Letters A, Volume 153, Number 6, 7, 11 March 1991

CONVERGENCE RATES AND DATA REQUIREMENTS FOR JACOBIAN-BASED
ESTIMATES OF LYAPUNOV EXPONENTS FROM DATA

S. Ellner
Biomathematics Program, and Department of Statistics,
North Carolina State University, Raleigh, NC 27695-8203, USA

A. R. Gallant, D. McCaffrey and D. Nychka
Department of Statics, North Carolina State University, Raleigh, NC 27695-8203, USA

Received 29 August 1990; accepted for publication 7 January 1991
Communicated by A. R. Bishop

Abstract

We present a method for estimating the dominant Lyapunov exponent from time-series data, based on nonparametric regression. For data from a finite-dimensional deterministic system with additive stochastic perturbations, we show that the estimate converges to the true values as the sample size increases, and give the asymptotic rate of convergence.