## 3 Results
Note that both the autocorrelation model and the trend change model were quite effective in interpolation (see Figure 4). The model constructed using the original rules, which does not directly incorporate the trend change and indirectly estimates it through autocorrelation, has R\({}^{2}\) = 0.810 fractions of the explained variance. This is higher than a  
Figure 3: Results of the comparison of the model of GDP dynamics of the Russian Federation (in constant prices), developed with the algorithm (**a**), and ARIMA (**b**). similar estimate of 0.726 for the ARIMA (0;2;0) model considered, and the ARIMA model shows the best results among the statistical methods we applied. However, the prediction accuracy of both models turned out to be low: they significantly underestimated the share of innovatively active organizations in 2020 (the created model predicted only 2.8% of innovatively active organizations estimated according to the 3 rd Oslo Manual methodology, and ARIMA 3.15%), which stabilized and even slightly increased (estimated according to the 3 rd Oslo Manual methodology to 6.29% from 5.30% in 2019). This once again proves the low quality of predictions of models of innovation during bifurcations. At the same time, the model built with the trend change in mind was not only more accurate in interpolation (R\({}^{2}\) = 0.875) but also less pessimistic in estimating the forecast for the next year (at 5.59%). In other words, the trend change model was obviously more effective in making forecasts and from the analytical point of view. As well as for the previsions dataset, we also compared the results of our algorithm with the results of the SSA + LSTM algorithm [8; 9]. This time, the dataset was even worse for LSTM network training. We had fewer data and we had many cycles with long periods that are hard for network estimation. Therefore, the result of the SSA + LSTM algorithm that we obtained by searching the best settings was an R\({}^{2}\) value of 0.198. This result does not indicate low effectiveness of the SSA + LSTM algorithm. This algorithm is simply not efficient enough to study data similar to the ones we are studying in this case. The results of calculating the quality of the models are shown in Table 1.  
The algorithm created made it possible not only to create a model that interpolates the available data accurately enough and made it possible to create a relatively accurate forecast; it also highlighted the trend and the three cyclical components. This has obvious analytical value, particularly making it possible to relate the high \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \begin{tabular}{c} **ARIMA (0,2,0)** \\ **As the Best of** \\ **Statistic Models** \\ **of the** \\ **Analyzed Data** \\ \end{tabular} & \
\begin{tabular}{c} **Algorithm with** \\ **the Base Rules** \\ **\end{tabular} &
\begin{tabular}{c} **Algorithm with** \\ **the Modified** \\ **Rules** \\ \end{tabular} & **SSA + LTSM** \\ \hline GDP dynamics & 0.973 & 0.985 & 0.992 & 0.960 \\ \hline Innovation activity in Russia & 0.810 & 0.726 & 0.875 & 0.198 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of the model comparison based on R\({}^{2}\). Figure 4: Results of comparison of the model of innovation activity in Russia developed with (**a**) the algorithm without the rule for trend change (Model 1), (**b**) with trend change (Model 2), and (**c**) ARIMA. economic processes and assess the peculiarities of the development of these processes by studying the behavior of these components.