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A linearization based non-iterative approach to measure the Gaussian noise level for chaotic time series. (English) Zbl 1271.65021

Summary: We propose a non-iterative method to determine the noise level of chaotic time series. For this purpose, we use the Gaussian noise functional derived by T. Schreiber [Phys. Rev. E 48, 13–16 (1993)]. It is shown that the noise function could be approximated by a stretched exponential decay form. The decay function is then used to construct a linear least squares approach where global solution exists. We develop a software basis to calculate the noise level which is based on TISEAN algorithms. A practical way to exclude the outlying observations for small length scales is proposed to prevent estimation bias. The algorithm is tested on well-known chaotic systems including Henon, Ikeda map and Lorenz, Rössler, Chua flow data. Although the results of the algorithm obtained from simulated discrete dynamics are not satisfactory, we show that it performs well on flow data even for extreme level of noise. The results that are obtained from the real world financial and biomedical time series are interpreted.

MSC:

65C60 Computational problems in statistics (MSC2010)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
37M10 Time series analysis of dynamical systems

Software:

GSL; TISEAN
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Full Text: DOI Link

References:

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