Bondarenko V. Modeling of time series using fractional Brownian motion

The thesis is devoted to the development of new mathematical models of objects described with the distribution of time data-time series . As a basic process in the proposed non-Markov models selected non-stationary process, fractional Brownian motion. By using the methods of probability theory and mathematical statistics, methods of system analysis and computational methods, new results have been obtained with respect to estimating model parameters, construction and testing the adequacy of the forecast models. According to a number of criteria proposed models have higher quality in comparison with the known. The developed methods and related algorithms are implemented in software tool, which is used for the analysis of real time data corresponding to the financial and biological objects.