Noise Level Estimation for a Chaotic Time Series

In this study, the correlation sum and the correlation integral for chaotic time series using the Supremum norm and the Euclidean norm are discussed. The correlation integrals are then used to deve...

[1]  Pengcheng Xu,et al.  A method of estimating the noise level in a chaotic time series. , 2008, Chaos.

[2]  Janusz A Hołyst,et al.  Noise-level estimation of time series using coarse-grained entropy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  F. Takens Detecting strange attractors in turbulence , 1981 .

[4]  A. Jayawardena,et al.  Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach , 2000 .

[5]  O. Rössler An equation for continuous chaos , 1976 .

[6]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[7]  Pengcheng Xu,et al.  Modified correlation entropy estimation for a noisy chaotic time series. , 2010, Chaos.

[8]  R. Smith,et al.  Estimating Dimension in Noisy Chaotic Time Series , 1992 .

[9]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[10]  K. Müller,et al.  Noise robust estimates of correlation dimension and K2 entropy. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  P. Xu,et al.  Neighbourhood selection for local modelling and prediction of hydrological time series , 2002 .

[12]  Diks,et al.  Efficient implementation of the gaussian kernel algorithm in estimating invariants and noise level from noisy time series data , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[14]  Schreiber Determination of the noise level of chaotic time series. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  C. Diks,et al.  Estimating invariants of noisy attractors. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Peter J.T. Verheijen,et al.  Influence of noise on power-law scaling functions and an algorithm for dimension estimations , 1997 .

[17]  Leonard A. Smith,et al.  Towards coherent estimation of correlation dimension , 2003 .

[18]  G. Ambika,et al.  A non subjective approach to the GP algorithm for analysing noisy time series , 2006 .