Scientific Journal of KubSAU

In the article the forecasting model which is based on the theory of cellular automatic machines and mathematical apparatus of indistinct sets is presented. Its work on the real data of time number productivities of sugar beet in Mostovskoy area of Krasnodar territory is shown

Tools and mathematical methods offered for usage represent essentially new base for forecasting of discrete evolutionary processes. Authors represent complete system of models and methods of temporary ranks’ with memory forecasting

The article discusses the impact of seasonal and event-component time series to assess the predictive performance of the tourist flow in Dombay village in the Karachay-Cherkessia Republic

The article studies the degree of "riskiness" of natural time series, which are inherent properties of the seasonal trend. The authors have made an analysis the result of which is the effect relationship between weather conditions and the dynamics of the behavior of the monthly volumes of mountain rivers

This article discusses the ways of reducing the financial, economic and social risks on the basis of an accurate prediction. We study the importance of natural time series of winter wheat yield, minimum winter, winter-spring daily temperatures. The feature of the time series of this class is disobeying a normal distribution, there is no visible trend

This work is devoted to the methods of multicriteria optimization and classical statistics of obtaining pre-estimated information for time series that have long-term memory, which is why their levels do not satisfy the independence property, and therefore the classical prediction methods may be inadequate. The developed methods of obtaining such information are based on classical statistics methods such as mathematical statistics, multicriteria optimization and extreme value theory. The effectiveness of the proposed approach has been demonstrated on the example of specific time series of volumes of mountain rivers

This article proposes a modification and training the Cellular Automaton predictive model. The author presents a modified system of models and methods for time series prediction with memory based on the theory of fuzzy sets and linear cellular automata

The present study was carried out in the view of the fact that there is no more or less complete theory of time series prediction memory to date. This determines the urgency and necessity of the development of new mathematical methods and algorithms to detect possible potential predictability of the series with the memory and the construction of adequate predictive models. Classical methods of forecasting economic time series are based on the mathematical apparatus of econometrics. It is carried out basing on the assumption that the observations that make up the projected time series are independent, whereby to perform the necessary subordination of the normal law. The latter, however, is the exception rather than the rule for economic time series that have so-called long-term memory. Toolkit implementations of nonlinear dynamics were the new computer technology that made it possible to study complex phenomena and processes “on the display screen”. The proposed approach differs from the classical methods of forecasting by the implementation of a new accounting trends (evolution of centers and the size of a bounding box), and is a new tool (phase portraits) to identify the cyclical components of the considered time series

It is offered to expand the classification of risks by introducing a global risk of economic system, which separates stages burdened with the local risks having arbitrarily direction. Serial or parallel origin of these risks is modeled dyadic chain vectors or four-dimensional conglomerates of quaternions in Clifford spaces. Multivariate risk is to transform analytically, calculate quantitatively, construct geometric vector operations in the ensemble with the economic variables on which part of the cost of the risk and that is lost or after symptoms appear. Therefore, the cost of an asset depends on a comprehensive cost of the "basis", burdened risk ("common value"), and the magnitude of the risk of leaving part - "risky value" - from zero. Now, the risk emerges as a new economic and mathematical category. Through the study of risks and through research of their new multi-dimensional performance value it is possible to insight into understanding the mechanisms of action of the economic laws worldwide and in Russia

The increase in volume of processed data and the rapid development of environmental monitoring, modeling, forecasting, analysis, visualization, prediction in modern conditions is connected with the consistent increase in their level of formalization. The bases for all this are requirements of significantly changed stochastics natural and economic processes. A new method of nonlinear dynamics, namely the method of sequential R/S-analysis is proposed. In the article, the authors paid attention to the method of fractal analysis of time series. The founder of fractal analysis is a British hydrologist H.E Hurst. He showed that natural phenomena such as river flows, rainfall, temperature, solar activity is followed by «biased random walk», i.e. trend with noise. The noise level and trend resistance are estimated in change in the normalized amplitude levels of the time series for the expiration time, or, in other words, how they entered a quantity called the Hurst exponent exceeds the value of 0.5. Rather essential information is a cyclical component to forecast. Thus, there is a need for further study of natural and economic processes based on the new mathematical models. These methods bring to forecast new useful methodological elements that are not in continuous methodology, concepts such as «noise color» persistence and anti-persistent series, Hurst, «long-term memory», R/S-trajectory and the trajectory of the Hurst exponent, etc.