## 3 Results  
The algorithm developed by the authors was initially tested on a generated dataset consisting of a polynomial trend, three harmonics, and a random component with negative autocorrelation with lag 1. The SSA method efficiently extracted all the main components, which allowed us to identify the types of dynamics with a high level of confidence and build a model that described with high accuracy the functions used to generate the dataset. After testing, the authors used the developed algorithm to analyze information about GDP and the number of researchers in the Russian Federation. The information for the analysis was taken from the website of the Federal State Statistics Service of the Russian Federation [22]. To build the model of GDP dynamics of the Russian Federation, the data for 1995-2020 were used; the data for 2021 were used as a test dataset, on the basis of which the quality of the forecast built by the created model was determined. To eliminate the effect of inflation, the data were adjusted to 2020 prices. The results of modeling were compared with several statistical methods, including trend-seasonal models SARIMA and ARIMA. Of these methods, ARIMA (0,2,0) provided the best results, and we used them as a basis for comparison with the developed algorithm results. The comparison with the methods of intellectual analysis, in our opinion, is not entirely correct since the final result of the developed algorithm is to obtain statistical models with a specific economic interpretation and not just the forecast itself. As a result of the work of the phasifier, it was found that it does not recognize fluctuations whose period is comparable with the length of the studied series of dynamics well enough. In our case, one of the highlighted SSA components was a cycle with a period of about 20 years (the Kuznets cycle), with a total length of the studied period of 26 years, and this cycle was not effectively recognized until we changed the rules to a set of estimates of the presence of the cycle according to data, first and second final difference, and periodogram. After introducing additional rules, the algorithm correctly recognizedthis long cycle (see Figure 2a). Then, a cycle model with a period of 22 years based on the sine function was constructed in automatic mode. Difficulties arose in study of the third component, recognized as random deviations with positive autocorrelation, but they were expertly estimated as cyclical fluctuations with a period of about 10 years (Juglar cycles). These cycles have a rather gentle growth and a sharp decline, which complicates their identification, recognition, and modeling. As a result, for effective recognition of such cycles, it was proposed to use in the phasifier an analogue of the Henderson filter to the selected components, which reduced the influence of possibly inaccurately defined values at the beginning and end of the components but does not significantly affect the overall result of recognition. Then, a rule based on detecting the cyclic direction of function change was added. This allowed us to identify this type of cycle and model it by index method (although it was possible to use other methods as well), which provided acceptable accuracy results of component recognition (see Figure 2b, unexplained variance fraction 48.2%). Since insufficient data do not allow modeling seasonal components by analogy with X-12, an alternative could be use of neural networks, but the possible quality of training on such a small dataset raises doubts about the reliability of the obtained result. The classical index method used in the study, on the other hand, is fairly easy to automate and reduces error associated with the decadal cyclic component. To evaluate the effectiveness of the algorithm developed in this study, we compared the created model with some statistical models, including models with polynomial trend, SARIMA and ARIMA models, and Fourier series decomposition (with maximum six series).