## 1 Introduction  
An important task arising in many areas of economic science and practice is analysis and prediction of the dynamics of processes and phenomena. At the same time, there are many approaches to solving these problems, particularly those based on application of statistical methods and methods of data mining. Such methods as trend extraction (for example, based on correlation and regression analysis) and cyclical fluctuations (both based on indices and Fourier series decomposition), as well as the simplest methods based on use of average values, in combination, can be considered as methods of unsupervised learning. In the same group, we can include the majority of methods of data mining, primarily using different types of neural networks, as the simplest direct propagation networks, and usually more effective in analysis of the dynamics (recurrent neural networks, fuzzy neural networks, and others). A number of other methods, such as those simulating random walk or using smoothing, moving averages, the more complex ARIMA method, and LOESS methods, are based on construction of part of the model totality. Sometimes, these parts are highlighted in a preliminary analysis, as in the X-12 method. These approaches make it possible to identify the main regularities in the dynamics of most phenomena and make a qualitative forecast, at least for the short- and medium term. However, in several sciences, particularly in economics, when studying the dynamics of some phenomena and processes, modeling becomes more complicated due to their characteristic chaotic behavior, a sharp change in trends, as well as the presence of a large number of different types of fluctuations that may vary over time. The reasons for such behavior may be the presence of many factors affecting the dynamics of the phenomenon under study and a complex, often cyclical nature of the relationship between these factorsas well as between them and the phenomenon under study. In such conditions, known methods do not have the necessary tools to build a predictive model with a high level of reliability of results. Indeed, methods based on analysis of the entire training totality (for example, correlation-regression analysis, Fisher's g test, fuzzy neural networks) can be ineffective in some cases because the trend and nature of fluctuations changed in the totality, which leads to low quality of obtained models. On the other hand, methods based on analysis of part of the training aggregate, such as the moving average or X-12, may be ineffective due to a lack of comprehensiveness of the obtained models. In economics, such phenomena, which are characterized by close to chaotic behavior, often occur in stock exchange analysis, analysis of tourist flows, as well as in many types of long-term analysis, for example, in long-term analysis of electricity consumption or economic activity of enterprises [1]. The influence of uncertainty is especially great in modeling of innovation activity, which makes modeling in this area especially difficult [2; 3]. Similar phenomena can be observed, for example, in forecasting of time series (TS) of crop yields, weather phenomena, availability of water resources, and so on [4]. When analyzing such phenomena, it seems effective to combine mathematical methods with methods of expert evaluation of existing trends (fundamental analysis), or to apply methods of intelligent data analysis. However, the results of applying expert methods not only depend significantly on the level of qualification of experts and their availability of the necessary information and tools but also lead to the risk of systematic errors, for example, in cases where experts are interested in this or that result of predictions. On the other hand, the prerequisites of the obtained results of intelligent analysis methods, such as different types of neural networks, are usually not transparent enough, which can lead to untraceable errors in determining the main trends and also not exclude system errors.