Estimation of the largest Lyapunov exponent for long-range correlated stochastic time series

2013 ◽  
Author(s):  
Oleg Gorshkov
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Long Range ◽  
Largest Lyapunov Exponent ◽  
The Largest Lyapunov Exponent ◽  
Stochastic Time Series ◽  
Stochastic Time

CHAOTIC ANALYSIS OF A TIME SERIES COMPOSED OF SEISMIC EVENTS RECORDED IN JAPAN

1994 ◽  
Vol 04 (01) ◽  
pp. 87-98 ◽  
Author(s):  
G.P. PAVLOS ◽  
L. KARAKATSANIS ◽  
J.B. LATOUSSAKIS ◽  
D. DIALETIS ◽  
G. PAPAIOANNOU
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Initial Conditions ◽  
Low Frequency ◽  
Underlying Mechanism ◽  
Largest Lyapunov Exponent ◽  
Seismic Events ◽  
Earthquake Dynamics ◽  
The Largest Lyapunov Exponent ◽  
Low Dimensional

A chaotic analysis approach was applied to an earthquake time series recorded in the Japanese area in order to test the assumption that the earthquake process could be the manifestation of a chaotic low dimensional process. For the study of the seismicity we have used a time series consisting of time differences between two consecutive seismic events with magnitudes greater than 2.6. The results of our study show that the underlying mechanism, as expressed by the time series, can be described by low dimensional chaotic dynamics. The power spectrum of the time series shows a power law profile with two slopes, α=1.4 in the low frequency and α=0.05 in the high frequency regions, while the slopes of the correlation integrals show an apparent plateau at the scaling region, which saturates at the value D≈3.2. The largest Lyapunov exponent was found to be ≈0.9. The positive value of the largest Lyapunov exponent reveals strong sensitivity to initial conditions of the supposed earthquake dynamics.

Quantifying Interactions in Nonlinear Feedback Dynamics: A Time Series Analysis

2019 ◽  
Vol 29 (01) ◽  
pp. 1950012
Author(s):  
Catherine Kyrtsou ◽  
Christina D. Mikropoulou
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Analysis ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Feedback ◽  
System Complexity ◽  
Feedback Mechanisms ◽  
Series Analysis ◽  
The Largest Lyapunov Exponent

In this paper, we further study the dynamics of the Kyrtsou model composed of heterogeneous nonlinear feedback rules. For various levels and types of underlying nonlinearity, we analyze the resulting time series by means of the largest Lyapunov exponent. Our results highlight that the observed interaction among feedback mechanisms cannot lead to a univocal interpretation of system complexity.

ON THE COMPUTATION OF LYAPUNOV EXPONENTS FOR DISCRETE TIME SERIES: APPLICATIONS TO TWO-DIMENSIONAL SYMPLECTIC AND DISSIPATIVE MAPPINGS

2000 ◽  
Vol 10 (12) ◽  
pp. 2791-2805 ◽  
Author(s):  
ELENA LEGA ◽  
GABRIELLA DELLA PENNA ◽  
CLAUDE FROESCHLÉ ◽  
ALESSANDRA CELLETTI
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Discrete Series ◽  
Dissipative Systems ◽  
Data Series ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Chaotic Motions ◽  
Conservative Systems ◽  
The Largest Lyapunov Exponent

Many techniques have been developed for the measure of the largest Lyapunov exponent of experimental short data series. The main idea, underlying the most common algorithms, is to mimic the method of computation proposed by Benettin and Galgani [1979]. The aim of the present paper is to provide an explanation for the reliability of some algorithms developed for short time series. To this end, we consider two-dimensional mappings as model problems and we compare the results obtained using the Benettin and Galgani method to those obtained using some algorithms for the computation of the largest Lyapunov exponent when dealing with short data series. In particular we focus our attention on conservative systems, which are not widely investigated in the literature. We show that using standard techniques the results obtained for discrete series related to area-preserving mappings are often unreliable, while dissipative systems are easier to analyze. In order to overcome the problem arising with conservative systems, we develop an alternative method, which takes advantage of the existing techniques. In particular, all algorithms provide a good approximation of the largest Lyapunov exponent in the strong chaotic symplectic case and in the dissipative one. However, the application of standard algorithms provides results which are not in agreement with the theoretical expectation for weak chaotic motions, and sometimes also for regular orbits. On the contrary, the method that we propose in this paper seems to work well for the weak chaotic case. Because of the speed of computation, we suggest to use all algorithms to cross-check the results.

scholarly journals Predicting the Price of WTI Crude Oil Using ANN and Chaos

2019 ◽  
Vol 11 (21) ◽  
pp. 5980 ◽  
Author(s):  
Tao Yin ◽  
Yiming Wang
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Crude Oil ◽  
Prediction Accuracy ◽  
Prediction Models ◽  
Bootstrap Method ◽  
Type Model ◽  
Largest Lyapunov Exponent ◽  
Ann Model ◽  
The Largest Lyapunov Exponent

This paper mainly studied the chaotic characteristics and prediction of WTI crude oil monthly price time series from January 1980 to June 2017. Meanwhile, we analyzed whether the major shock of the financial crisis in July 2008 would break the chaotic character of the time series. In addition, when using the largest lyapunov exponent to determine chaotic characteristics, the robustness test of the largest lyapunov exponent was carried out using bootstrap method. Then, we utilized three types of prediction models (ANN+Chaos-type models, Chaos-type model and ANN-type models) to predict the price of crude oil in different months. And we found that the prediction accuracy of ANN-type model is lower than the other type models. This indicated that the accuracy of the prediction with ANN model under the model misspecification is not high because the time series of WTI crude oil price has chaotic characteristics. At last, we constructed a new predictive model, namely HWP-CHAOS model, to compare the prediction accuracy of the above three type models, and discovered the best prediction model among these models is HWP-CHAOS model.

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