## 2 Materials and Methods  
To solve the problems of forecasting complex economic and innovation processes in conditions of uncertainty, the authors propose to use a combined approach to build a multi-component model of their dynamics. Similar algorithms are used in radio engineering [12], which makes it possible to increase the efficiency of control and management processes in a competitive environment of functioning of adaptive information transmission systems, as well as to create support for the process of adaptive control of the state of radio devices. As a similar process control tool for its application in the field of economics, we propose an algorithm, reflected in Figure 1.  
The algorithm consists of the following steps:  
1. Selection of time series components using the SSA method. For these calculations, we used the Pots package [13]. 2. Creation of fuzzy estimates of the possible character of time series components on the basis of search analysis tools and empirical rules. This estimation takes place in the module \"phasifier\" and can be performed both in automatic mode and corrected by expert method taking into account the proposed automatic estimations. These calculations were performed using packages NumPy, ScPyPy, and Pandas. The package Matplotlib was used for visualization. 3. The dynamic expert system, based on fuzzy logic, draws conclusions about the optimal classification for each component of the time series. At the same stage, the expert system can draw conclusions from the subject area, concerning, for example, the possible economic content of each component. In addition to the previously mentioned tools, we used FisPro 3.8 [14] to visualize and verify the calculations. 4. Expert system evaluations can be made in the form of fuzzy logic, in which case they must go to the defuzzifier to obtain clear evaluations. 5. Based on clear estimates, the optimal model of each component is selected and constructed, taking into account its type and possible economic content. 6. A generalized model, which can be used for analysis and forecasting of economic and innovative processes, is constructed. Let us consider the above steps in more detail. Separation of the dynamics components allows us to consider SSA as a method of exploratory analysis, application of which is highly effective in cases where a dynamics series may include a large number of different components with insufficiently accurately studied properties. For example, as shown in [7], in many time series describing the dynamics of innovation activity in the Russian Federation and Volgograd region for twenty years, we can distinguish a trend, two cyclic components (with the period of about 3 years and about 8 years), as well as various types of autocorrelation and, of course, \"white noise\". This agrees with the general theoretical ideas about the structure of series of dynamics in the economy, in which analysis of the dynamics by years traditionally distinguishes short-term cycles of Kitchin (with a period of 2-4 years); medium-term economic cycles of Juglar with a period of 7-11 years and long-term cycles of Kuznets (period 15-25 years) and Kondratiev (period 45-60 years), while long-term cycles in our study [7] were not distinguished because of the limited length of time series. Before we start to use SSA method, we should set window's length L [15]. Large values of L allow reconstructing long period oscillations, but too large values of L leave very few observations to make qualitative reconstruction. Therefore, L usually takes a value from quarter to half the time series length (N/4... N/2) [16]. We can also examine the median value [17] as the optimal L value. Figure 1: A generalized structural diagram of the dynamics analysis based on fuzzy processing of time series components obtained with SSA. The SSA method consists of two phases, decomposition and reconstruction [18]. Let us consider these stages of the method. The first stage of decomposition phase is embedding.