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Lyapunov exponents as a nonparametric diagnostic for stability analysis
Author(s) -
Dechert W. D.,
Gencay R.
Publication year - 1992
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.3950070505
Subject(s) - lyapunov exponent , lyapunov function , nonparametric statistics , nonlinear system , stability (learning theory) , dynamical systems theory , computer science , function (biology) , series (stratigraphy) , mathematics , control theory (sociology) , econometrics , control (management) , artificial intelligence , machine learning , chaotic , physics , quantum mechanics , paleontology , evolutionary biology , biology
The common observation made in the empirical nonlinear dynamics literature is the constraints imposed by the availability of a limited number of observations in the implementation of the existing algorithms of Lyapunov exponents. The algorithm discussed here can estimate all n Lyapunov exponents of an unknown n ‐dimensional dynamical system accurately with limited number of observations. This makes the algorithm attractive for applications to economic as well as financial time‐series data. The implementation of the algorithm is carried out by multilayer feedforward networks which are capable of approximating any function and its derivatives to any degree of accuracy.