J. E. Sandubete Galán, L. Escot Mangas
A relevant field inside chaos theory is the detection of a chaotic behavior from empirical time series. Most of the methods and techniques related to test the hypothesis of chaos from a time series tries to quantify well-known chaotic sensitivity to initial conditions property estimating the so-called Lyapunov exponents. This paper provides new robust statistical methods for estimating the Lyapunov exponents on a noisy environment by Jacobian indirect algorithms. Initially, the Jacobian indirect methods focused on linear regressions. Later, other types of nonlinear regression models were used as, for example, neural network models. These existing indirect Jacobian methods share, however, a common feature. They are all global methods. The main objective of this paper is to extend these global neural nets methods, by using two local alternatives: a local polynomial kernel regressions and a local neural net kernel model. We apply such methods to several noise-contaminated time series.
Keywords: Chaotic time series, Lyapunov exponents, Local Jacobian indirect methods, Polynomial kernel models, Neural net kernel models
Scheduled
Time series
June 9, 2022 5:10 PM
A11
