ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 5. Vol. 25. 2019

DOI: 10.17587/it.25.300-312

N. T. Abdullaev¹, Ph. D., Head of Department, e-mail: a.namik46@mail.ru, O. A. Dyshin², Ph. D., Associate Professor, I. D. Ibrahimova¹, Assistant, e-mail: irada432@gmail.com, Kh. R. Ahmadova¹, Ph. D., e-mail: yubaba66@hotmail.com,
¹Azerbaijan Technical University,
²Azerbaijan State Oil and Industrial University

Segmentation of Non-Stationary Physiological Signals with Fractal Properties

Segmentation is usually understood as the task of separation an available time series into segments (periods) with different dynamics.
If we present the behavior of a complex system with an adequate model, then the transition process will correspond to the transition of model parameters in the state space from one stable phase trajectory to another.
In the case of a sufficiently large number of countdown in the sample and the number of realizations of the dynamic series, the procedure of segmentation of a signal into stationary fragments should give unambiguous results. If compare the distributions and dispersions in two successive fragments of a time series, then at the point of their junction, can state a violation of the stationarity of the process in the narrow sense.
Evaluation of the statistical properties of the physiological signal is possible, however, only on a certain finite time interval. At the same time, the estimated interval can be reduced by increasing the number of samples per unit of time due to the higher frequency of digitization of the studied continuous physiological process only up to a certain limit: until the moment when neighboring counts become strongly correlated. It is this circumstance that limits the possibility of distribution the theoretical definition of stationarity to real physical processes, therefore the concept of "quasi-stationarity" was introduced into practice, highlighting the understanding of stationarity in such a restrictively evaluative aspect.
Presence of self-similarity, i.e. scale invariance in relation to the main statistical characteristics leads to continuous repetition in the self-similarity interval of the properties of some components of the studied dynamic series, meaning that these components are not informative for assessing the changes.
The most free from various restrictions is the method of self-similarity assessment, based on discrete wavelet transform of the dynamic series in the framework of multiresolution analysis. Using the sum of the components of the original time series reconstructed from the wavelet decomposition, the fractal component is selected with the determination of the self-similarity depth of the random process under study and an estimate of its trend component is found.
Using the regression model of a time series with volatility represented by a dynamic series after rejection (removal) of its trend component, it is possible to determine change-points of volatility, which divide the initial series into quasistationary segments corresponding to the volatility function jumps. For this purpose, a special computational procedure is applied, which generalizes the iterative method of centered cumulative sums of squares.
Keywords: fractals, wavelet expansion, nonstationarity, time series, volatility

P. 300-312

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