The Dissertation thesis is dedicated to elaboration of elements of mathematical software for dealing information systems realizing the procedure of forecasting models construction based on analysis of statistic properties of dynamic series. Mathematical forecasting model of stochastic dynamic series with the consideration of a forecast error, synthesized based on the research of methods of exponential smoothing and their modifications, autoregress integral moving average (ARIMA) and under conditions of disturbing factors has been received in the dissertation for the first time. For the first time, mathematical forecasting models have been obtained for foreign exchange currency rates for increasing and declining portions of the temporary series with the assistance of NN, which together with the results of the technical analysis decreased the value of market risks. Scientific results, received in the dissertation theses are practically applied in scientifically research institute "NIPI ASU TRANSGAZ" and at the Kharkiv Forex-Club, as well as when developing mathematical software for automatic control systems (ACS) for many subject fields.