time series

Purpose. The aim is to reveal the dependence of Granger causality results on chosen time scales of constructed empirical models in application to the task of investigation of evolution of coupling between brain areas during limbic seizures.

A contemporary consideration of such concepts as dimension and entropy of dynamical systems is given. Description of these characteristics includes into the analysis the other notions and properties related to complicated behavior of nonlinear systems as embedding dimension, prediction horizon etc., which are used in the paper. A question concerning the application of these ideas to real observables of the economical origin, i.e. market prices of the companies Schlumberger, Deutsche Bank, Honda, Toyota, Starbucks, BP is studied.

Transfer entropy is widely used to detect the directed coupling in oscillatory systems from their observed time series. The systematic error is detected, while estimating transfer entropy between nonlinear systems with K-nearest neighbours method.

Signals obtained from most of real­world systems, especially from living organisms, are irregular, often chaotic, non­stationary, and noise­corrupted. Since modern measuring devices usually realize digital processing of information, recordings of the signals take the form of a discrete sequence of samples (a time series). The present paper gives a brief overview of the possibilities of such experimental data processing based on reconstruction and usage of a predictive empirical model of a time realization under study.

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the wavelet­based methods in geophysics is also considered.

The paper is devoted to the history of physics and evolutionary biology to economics. This influence began with the birth of economics as a separate field of scientific knowledge and changed  with the development of physics and biology. Strengthening the role of statistical methods in the  physics of the twentieth century, the birth of nonlinear physics, biology, evolution is reflected in the  economy and finance, resulting in the appearance of such area as econophysics, nonlinear and  evolutionary economics.

A comparation of wavelets and empirical modes concepts is performed that represent the most perspective tools to study the structure of nonstationary multimode processes. Their advantages over the classical methods for time series analysis and restrictions of both approaches are discussed that needs to be known for correct interpretation of the obtained results. New possibilities in the study of signals structure at the presence of noise are illuctrated for digital single­channel experimental data of prospecting seismology.

The new method for the calculating of the spectrum of the Lyapunov exponents from data series is proposed. The already known methods of the same thematic are investigated. The Roessler system is given as an example for describing the proposed method. The results of numerical modeling are presented.

The problem of detection and quantitative estimation of directional couplings (mutual influences) between systems from discrete records of their oscillations (time series) arises in different fields of research. This work shows that results of the traditional «Granger causality» approach depend essentially on a sampling interval (a time step). We have revealed the causes and character of the influence of a sampling interval on numerical values of coupling estimates.

The problem of compact mathematical model reconstruction of short electroencephalogram tracings during epileptic seizure is solved. This kind of model map can be useful in many applications, for example, in time series segmentation with following clustering of obtained fragments. Optimization methods are proposed as a solution. It is shown that application of optimization methods allows to obtain adequate model at that time decreasing number of modeling map basis functions.