A linearization based non-iterative approach to measure the gaussian noise level for chaotic time series

Çoban, Gürsan; Büyüklü, Ali Hakan; Das, Alaka

doi:10.1016/j.chaos.2011.10.011

Cited by 12 publications

(8 citation statements)

References 31 publications

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“…Bask considered Swedish Kroner versus Deutsche Mark, ECU, US$, and Yen in his study using data of daily observation and found indication of deterministic chaos in all exchange rate 2 Economics Research International series [6,7]. In a series of works (2007,2012, and 2013), we investigated and confirmed the chaotic property of foreign exchange rates of several countries [8][9][10][11]. Chaotic processes are characterized by positive Lyapunov Exponents (LEs) and we calculated LEs from ForEx data.…”

Section: Introductionmentioning

confidence: 86%

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Investigating the Existence of Chaos in Inflation Data in relation to Chaotic Foreign Exchange Rate

Das

Das²

2014

Economics Research International

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Foreign exchange (ForEx) rates are amongst the most important economic indices in the international monetary markets. ForEx rate represents the value of one currency in another and it fluctuates over time. It is related to indicators like inflation, interest rate, gross domestic product, and so forth. In a series of works, we investigated and confirmed the chaotic property of ForEx rates by finding positive largest Lyapunov exponent (LLE). As inflation influences ForEx, in this work we would like to address the specific question, Is inflation data also chaotic? We collected data for time period of 2000 to 2013 and tested for nonlinearity in data by surrogate method. Calculating LLE, we find existence of chaos in inflation data for some countries.

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Section: Introductionmentioning

confidence: 86%

“…Chaotic processes are characterized by positive Lyapunov exponent (LE) calculated following the approach of Wolf et al [24] as detailed in Das et al [8,9]. Again, we used the TSTOOL [22] to find the LLE.…”

Section: Finding Lyapunov Exponent Using Tstool Packagementioning

confidence: 99%

Investigating the Existence of Chaos in Inflation Data in relation to Chaotic Foreign Exchange Rate

Das

Das²

2014

Economics Research International

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“…x n+1 = 1 − ax 2 n + y n y n+1 = bx n , where a = 1.4 and b = 0.3. This map has been widely used in the literature to numerically characterize different methods devoted to estimate attractor's invariants [26,23,20,6,28,22,19,25,16,4]. For this map, and the given parameters values, the correlation dimension and correlation entropy are D= 1.22 and K 2 = 0.3, respectively [28].…”

Section: Noise Level Functionalmentioning

confidence: 99%

Automatic estimation of attractor invariants

Restrepo

Schlotthauer

2017

Nonlinear Dyn

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The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new coarse-grained estimators for the correlation dimension and for the correlation entropy. They can be easily estimated from the calculation of two U-correlation integrals. We have also developed an algorithm that is able to automatically obtain these invariants and the noise level in order to process large data sets. This method has been statistically tested through simulations in low-dimensional systems. The results show that it is robust in presence of noise and short data lengths. In comparison with similar approaches, our algorithm outperforms the estimation of the correlation entropy

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“…It is worthy of being mentioned that, Brown, Bryant and Abarbanel (BBA) [Brown et al, 1991] developed an excellent method to exactly estimate Lyapunovexponent spectrum from clean time series using local neighborhood-to-neighborhood mappings with higher-order Taylor series. In fact, all these methods will form a great challenge for the experimental data because the signals from real-world systems are unavoidably contaminated with noise [Coban et al, 2012;Urbanowicz & Holyst, 2006]. So, different kinds of methods for estimating Lyapunov exponents from noisy time series are studied by many researchers.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov-Exponent Spectrum From Noisy Time Series

Yao

Liu

et al. 2013

Int. J. Bifurcation Chaos

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Since all kinds of noise exist in signals from real-world systems, it is very difficult to exactly estimate Lyapunov exponents from this time series. In this paper, a novel method for estimating the Lyapunov spectrum from a noisy chaotic time series is presented. We consider the higher-order mappings from neighbors into neighbors, rather than the mappings from small displacements into small displacements as usual. The influence of noise on the second-order mappings is researched, and an averaging method is proposed to cope with this noise. The mappings equations of the underlying deterministic system can be obtained from the noisy data via the method, and then the Lyapunov spectrum can be estimated. We demonstrate the performance of our algorithm for three familiar chaotic systems, Hénon map, the generalized Hénon map and Lorenz system. It is found that the proposed method provides a reasonable estimate of Lyapunov spectrum for these three systems when the noise level is less than 20%, 10% and 7%, respectively. Furthermore, our method is not sensitive to the distribution types of the noise, and the results of our method become more accurate with the increase of the length of time series.

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A linearization based non-iterative approach to measure the gaussian noise level for chaotic time series

Cited by 12 publications

References 31 publications

Investigating the Existence of Chaos in Inflation Data in relation to Chaotic Foreign Exchange Rate

Investigating the Existence of Chaos in Inflation Data in relation to Chaotic Foreign Exchange Rate

Automatic estimation of attractor invariants

Lyapunov-Exponent Spectrum From Noisy Time Series

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