Scientific Journal of KubSAU

In the process of formation of nonlinear dynamics, the scientific society was able to refute the classical mechanisms of Newton-Laplace by justifying the chaotic nature of the phenomena of the world. However, despite the emergence of new mathematical models and tools, forecasting of nonlinear systems is a difficult task, as not only the quantitative and qualitative characteristics of the factors affecting the system are unknown, but also there is a problem of a small amount of information for forecasting. In this article, the authors consider the linear cellular apparatus as a tool for prediction the final state, to which the system will come based only on its output indicators of previous years. Since the use of a linear cellular automaton for prediction of nonlinear systems is an assumption of the authors, it should be tested on the series of stochastic systems exposed to different risk factors, which together give either a positive response of the system or a negative one. An example of such series is the time series of yields, as it is affected by climatic conditions, the appearance of which, in turn, is also difficult to predict. Prediction of stochastic systems using linear cellular automaton really makes it possible to get adequate and visual models. Due to the fact that the forecast model has a discrepancy with the real result of 0-15% (both positive and negative), the conclusion is that the predicted value will help either to take measures to ensure that the real value in the future is not lower, or to make sure that the decisions and measures taken are correct, when a value is higher than the forecast

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

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

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

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 lack of a unified research platform and tools for various sectors of Russian economy, allowing to take into account the specifics of the object of study, significantly slows down and complicates the decisionmaking processes, at the same time thereby reducing their efficiency, which is even more negative in terms of the need of quick decisions of the tasks on import substitution. Scientific essence of the proposed research can be formulated in the form of innovative unified research platform, showing the interrelated causal system components, theoretical and practical, analytical and experimental units, productive activities which are scientifically proven smart products for various sectors of the Russian economy. The constantly changing economic environment makes to answer its idempotent mathematics and information paradigm, theory, methodology. Here it is important to select the structure and rationale of the proposed research mathematical "platform". A new, different but mutually complementary multi-criteria approaches, a set of economic-mathematical models and modern mathematical and instrumental constructs, monitoring, comparison, and generalization of the results is needed. In the article it is shown that the proposed use of instrumentation and mathematical methods represent essentially new base for forecasting of discrete evolutionary processes

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.

The work used methods of system analysis, monographic, structural and logical, economic-statistical, mathematical continuous and discrete, settlement and constructive methods as well as software tools of linear cellular automata. Usage of each method was based on their functionality, thus ensuring the accuracy of the findings and scientific positions. In this article we attempt to predict the dynamic behavior of the financial market elements, to use on the basis of a linear cellular automaton computer tools and methods of nonlinear science for adequate numerical reflection measure various risks, primarily financial and economic risks, as well as to show the power of computer graphics, computer mathematics system linear cellular automata, to emphasize an important philosophical role of visualization. The authors of the work programmed linear cellular automaton based on Python 2.7 software platform in the form of application. The program validates the predictive model on the adequacy of the selected coloring, is forecast error and builds polygons predictive model and input data on the same graph. The proposed research area is relevant to the processes in the financial and economic system, bringing in useful innovative elements in the generalized forecast that do not exist in continuous classical methodology

Development of monitoring of the behavior of financial market, simulation, analysis, visualization, prediction in modern conditions is connected with a consistent increase in their level of formalization. The basis for this process is the requirements of significantly changed (in the direction of increasing) stochastics, turbulence, volatility, financial and economic processes. Particular relevance in the analysis of behavior of economic time series elements of the financial market is now becoming more systematic development of diverse, interdependent and mutually complementary economic and mathematical models. The models are linked, they are operating on the same source material, and their selection has improved the representativeness of the algorithms of modern economic processes of the financial market, which is important for transformational (transitional) market economies. In the article it is shown that the proposed usage of instrumentation and mathematical methods represent essentially new base for forecasting of discrete evolutionary processes

In the context of the objective existence of risk and economic, human and other losses related with it, there is a need in a specific mechanism, which would allow the best way to predict the damage caused by the emergency. These risk management tools in emergency situations are monitoring and forecasting. In this research work, time series are used as a signal; they contain information about the number of fires in the Karachayevo-Cherkessia in the period of 1983- 2014. In solving the problem, the authors applied wavelet tools for data cleaning from noise, anomalies that have provided quality model building reliable forecast - possible number of fires in one quarter ahead. This example shows that for the construction of this forecast there is no need for a rigorous mathematical model specification, which is especially valuable in the analysis of poorly formalized processes. We have noted that most of the tasks in emergencies fall into this category of processes