Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data

S. Ellner; Andrew Ronald Gallant; D. McCaffrey; D. Nychka

doi:10.1016/0375-9601(91)90958-B

Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data

S. Ellner, Andrew Ronald Gallant, D. McCaffrey, D. Nychka

Economics

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

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.

Original language	English (US)
Pages (from-to)	357-363
Number of pages	7
Journal	Physics Letters A
Volume	153
Issue number	6-7
DOIs	https://doi.org/10.1016/0375-9601(91)90958-B
State	Published - Mar 11 1991

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1016/0375-9601(91)90958-B

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title = "Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data",

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.",

author = "S. Ellner and Gallant, {Andrew Ronald} and D. McCaffrey and D. Nychka",

year = "1991",

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T1 - Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data

AU - Ellner, S.

AU - Gallant, Andrew Ronald

AU - McCaffrey, D.

AU - Nychka, D.

PY - 1991/3/11

Y1 - 1991/3/11

N2 - 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.

AB - 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.

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DO - 10.1016/0375-9601(91)90958-B

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AN - SCOPUS:0001414087

SN - 0375-9601

VL - 153

SP - 357

EP - 363

JO - Physics Letters A

JF - Physics Letters A

IS - 6-7

ER -

Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data

Abstract

All Science Journal Classification (ASJC) codes

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