Zrazhevsky O. Systems approach to recovery of functional dependence of non stationary time series with various structures

Dissertation is devoted to the development of systems approach to estimation of functional dependences of non-stationary time series of different structure using methodology, improvement, developments and mathematical foundation of statistical methods of modelling of time series with long-range dependence and in the case of boundedness of empiric information. The method for prediction of long-range dependent time series is formulated. The method of stage-by-stage regression is developed and mathematically grounded. The theory of selection of the optimal regression model complexity, that is based on the estimates of the rate of uniform convergence of the empirical risk functional to the theoretical, is generalized. The complex of program modules, that realizes methods and algorithms of processing and analysis of data on the basis of the results mathematically grounded in the work, is created. Practical application of the offered systems approach is pointed for solving of practical tasks of time series analysis on the examples of the artificial data and time series of credits, given to juristic persons in Kherson, Sumskiy areas and in Crimea.