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

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

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 rapidly changing conditions of the modern world, analysts and decision makers are in need to use new formal means of analysis and evaluation of alternatives problems. This work is dedicated to the development of such tools. The article presents a detailed analysis and technical and economic characteristics of the subject area - the financial market and its specific components - the value of a time series of gold, silver, palladium, platinum, and two kinds of exchange rates: EUR / RUB, USD / RUB. The authors have proposed a 5-criteria economic-mathematical model of the main components of the ranking of the financial market. The authors argue the impossibility of using a single integrated set of criteria for the replacement of the criteria or the use of criteria convolution procedures as the standard procedure of solving the problem of multi-criteria optimization. It demonstrates that such criteria as criteria for "risk" must be considered as an estimate of the degree of deviation from the expected value of the possible values of this criterion. The practical significance of the results is determined by the fact that the main points, conclusions, recommendations, models and methods can be used in order to improve the management and planning of development strategies of banking systems, trading platforms, as well as by developers of information and analytical systems to support management decisionmaking

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

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

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

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.

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

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