Titre :

Testing for non-chaoticity under noisy dynamics using the largest Lyapunov exponent

Auteur(s) :

Gatfaoui, Hayette [Auteur correspondant]
Lille économie management - UMR 9221 [LEM]
IÉSEG School Of Management [Puteaux]
de Peretti, Philippe [Auteur]
Centre d'économie de la Sorbonne [CES]

Titre de la revue :

Soft Computing

Pagination :

8617–8626

Éditeur :

Springer Verlag

Date de publication :

2019-12-18

ISSN :

1432-7643

Mot(s)-clé(s) en anglais :

Noise
Confidence intervals
Simulation smoother
Kalman filter
Chaoticity
Largest Lyapunov exponent

Discipline(s) HAL :

Mathématiques [math]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Sciences de l'Homme et Société/Gestion et management

Résumé en anglais : [en]

In this paper, we introduce a robust procedure to test for non-chaoticity when data are contaminated by an additive noise. Under the Kalman filter framework, our procedure first amounts to compute the largest Lyapunov ...
Lire la suite >In this paper, we introduce a robust procedure to test for non-chaoticity when data are contaminated by an additive noise. Under the Kalman filter framework, our procedure first amounts to compute the largest Lyapunov exponent of the extracted signal. The exponent describes the log-divergence of a dynamical system (Rosenstein et al. in Phys D 65(1–2):117–134, 1993. https://doi.org/10.1016/0167-2789(93)90009-p). Then, using the so-called simulation smoother, we generate a high number of trajectories of the state-vector, conditional on the observed series, and compute the empirical distribution of the largest Lyapunov exponent. The distribution allows for computing confidence intervals. We can thus test if the largest Lyapunov exponent is not significantly greater than zero. Using Monte Carlo simulations, we show the validity of such an approach. We provide an illustration using toy models, which depict several dynamical systems. Finally, we implement tests of non-chaoticity on financial time series. We find no empirical evidence of chaotic patterns. Our approach is simple, efficient, and tests for chaos when data are measured with errors (i.e., noisy dynamics)Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Lille Économie Management (LEM) - UMR 9221

Source :

Harvested from HAL