Deineko Z. Methods of analysis of nonstationary self-similar time series, based on the discrete wavelet transform

Research object - the self-similar processes in technical, information and biological systems. A research objective - working out the computational methods for analyzing of non-stationary self-similar fractal structure of time series based on the discrete wavelet transform, which will improve the accuracy of self-similarity parameter estimation in biological, information and technical systems. Research methods: the methods of the fractal and the statistical analysis of the data at research of properties of self-similarity and calculation of statistical characteristics; methods of the probability theory and stochastic processes for modeling self-similar processes; methods of the wavelet-analysis for structure research and self-similarity of time series. Research apparatus: personal computer. Theoretical and practical results - the developed methods of research of the self-similar processes can be used for modeling and the analysis of technical, information, biological and other systems, as well as monitoring of the critical phenomena in the dynamic systems, which possess the property of self-similarity. The results of work are supposed to be used at the analysis of time sequences, where the self-similar structure and long-term dependence influence the statistical characteristics of investigated processes. Scientific novelty - for the first time there was proposed the approach to estimation of the degree of self-similarity by means of the discrete wavelet transform, based on the correlation analysis of Hurst exponent estimators, thus improved the accuracy of the estimation in time series of short length; there has been the further development of the method of Hurst exponent estimators on the basis of discrete wavelet-transform in the field of construction interval estimations which characteristics, in contrast to existing methods, taking into account the length of the self-similar time series and the type of mother wavelet function; for the first time there was offered the method of Hurst exponent wavelet estimation for time series with considerable trend and cyclic components, which is based on the analysis a component of wavelet-energy spectrum, that allows to raise accuracy of estimations; there was developed the preliminary analysis of the spectrum of wavelet-energy and the choice of effective parameters of the mother wavelet-function, which unlike existing methods, takes into account the relation of the fractal noise and the trend component, and creates preconditions for improvement of the computational properties of the basic method of estimation. The research results were introduced: in state budgetary research work carried out according to thematic plan of scientific research of Kharkov National University of Radio Electronics, financed by the Ministry of Education and Science, youth and sports of Ukraine; in the Ukrainian scientific research institute of environmental problems (the certificate of implementation from 25.11.2011), in joint-stock association "Energooblik" (the certificate of implementation from 20.01.2012); and also into the educational process at the chairs of program engineering (the certificate of implementation from 07.03.2012) and media systems and technologies (the certificate of implementation from 18.01.2012) in Kharkov National University of Radio Electronics that is confirmed by corresponding certificates.