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Two approaches to extraction of information from time series.

Time series analysis (signal processing) is a large applied discipline which includes many techniques and approaches. They can be systematized in different ways: linear and nonlinear, parametric and non-parametric, based on construction of a mathematical model and "direct" (dispensing with modeling).

As for the latter systematization, one can consider the following methods as "direct":

1) Traditional statistical analysis which includes calculations of mean values, variances, correlation function, probability distribution function, etc;

2) Fourier-analysis and wavelet analysis belong to a wide family of the so-called "linear" methods since they give complete characterization of linear processes;

3) Nonlinear methods include reconstruction of phase orbit from time series, estimation of fractal dimensions, entropies, Lyapunov exponents, etc.

Methods based on model construction historically and logically can be divided into to big groups:

1) Construction of linear stochastic models (the most popular among them are autoregressive - moving average models). This field has been called "system identification".

2) Construction of nonlinear dynamical models (as a rule, maps or ordinary differential equations). It relies on ideas and techniques of nonlinear dynamics. Therefore it is called "reconstruction of dynamical systems".


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  9. Chaos and Its Reconstructions // Eds. G. Gouesbet, S. Meunier-Guttin-Cluzel, O. Menard. Nova Science Publishers, New York, 2003.
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  11. Anishchenko V.S., Astakhov V.V., Vadivasova T.Ye., et al. Nonlinear effects in chaotic and stochastic systems. Moscow-Izhevsk, ICR, 2003.
  12. Bezruchko B.P., Smirnov D.A. Mathematical modeling and chaotic time series. Saratov, "College", 2005. 320 p.

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