Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms

Lorenzo Escot and Julio E. Sandubete

Applied Mathematics and Computation, 2023, vol. 436, issue C

Abstract: Most of the existing methods and techniques for the detection of chaotic behaviour from empirical time series try to quantify the well-known sensitivity to initial conditions through the estimation of the so-called Lyapunov exponents corresponding to the data generating system, even if this system is unknown. Some of these methods are designed to operate in noise-free environments, such as those methods that directly quantify the separation rate of two initially close trajectories. As an alternative, this paper provides two nonlinear indirect regression methods for estimating the Lyapunov exponents on a noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with the methods using local networks obtaining more accurate results than those using local polynomials.

Keywords: Chaotic time series; Lyapunov exponents; Jacobian indirect methods; Global and local neural net models; Local polynomial kernel models; Local neural net kernel models (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005720

DOI: 10.1016/j.amc.2022.127498

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