This paper reviews main approaches to risk assessment. The authors accented attention on the nonlinear approach to the theory of risks. It is proposed to define economic risk as the probability of threats that could have material adverse effect on the economic system under study and to change its current state. The method and the program product designed by the authors integrate a wide range of indicators of economic and financial activities at the regional level in the program-technical complex. This paper describes a new method for assessing synergistic and prediction of risk over long time rows of economic indicators at the regional level, including methods of nonlinear and chaotic dynamics, enabling a pseudo-phase and phase portraits, to determine the volatility, to calculate fractal characteristics and predict the behavior of socio-economic indicators with modernized method of Hurst, to model based on recovery probability distribution function of nonequilibrium potential function, to determine the local and global stability of the regional economy and to identify risks as the probability of the threats of an economic nature.

In the article, a synergetic method of the economic time series forecasting on the basis of the modified method of Hurst is discussed. It is a new nonlinear method of predicting the development of economic systems according to time series on macro- and mesolevels. The main theorem underlying the forecasting method is formulated and strictly proved: for a chaotic series of a particular length it is possible to specify a time interval where the series is reliably predicted with the Hurst exponent more than 0.5. The examples of the fractal characteristics’ calculation and the forecasting taking into account time of reliable forecast of the socioeconomic indexes’ behavior — oil prices, natural gas prices, the Dow Jones index, the «euro-dollar» prices, the Gross Domestic Product, and some other indicators at the regional level are given. All calculations are carried out by means of the specialized software product upgraded for the task solution set in this article.