Forecasting the Industrial Development of the Russian Federation: a Comparative Analysis of Mathematical Tools

The purpose of this paper is a comprehensive comparative analysis of various mathemati-cal methods for forecasting a key index of industrial development – the value added of industry in the Russian Federation. The research aims to assess the effectiveness and accuracy of tradi-tional and modern approaches in the context of real, crisisprone economic dynamics. Determin-ing the most reliable tools for making medium-term forecasts is important to increase the validity of macroeconomic decisions. The empirical basis of the study was the official statistics of the World Bank for the peri-od from 2002 to 2021. Indexes such as industrial value added, gross capital formation, and the share of medium- and high-tech exports were selected for modeling. To ensure stationarity and eliminate the trend component, all-time series were transformed using second differences, which was confirmed by the Dickey-Fuller test. The comparative analysis was carried out between three methods: the method of extrapolation based on historical trends, a multifactorial linear economet-ric model estimated by the least squares method, and a neural network model with long short-term memory (LSTM). The quality of the models was assessed by comparing forecasts for the periods 2011-2012 and 2019-2021 with actual data. The results of the study revealed a significant superiority of modern methods over tradi-tional extrapolation, which gave a significant and increasing range of forecast values. The econ-ometric model showed significantly higher and more stable accuracy, adequately reflecting the main linear dependencies. The best results were demonstrated by the LSTM model, which most accurately predicted the trajectory of recovery after the 2008-2010 crisis and correctly recorded a slowdown in growth ahead of the 2020 crisis. However, none of the models was able to predict the extreme recession of 2020 caused by the global external shock (the COVID-19 pandemic), which indicates the limitations of any formalized approach in the face of unforeseen structural changes. The analysis makes it possible to conclude that deep learning architectures, in particular LSTM models, are highly effective and promising for forecasting complex macroeconomic in-dexes. These models are capable of establishing nonlinear dependencies and longterm effects in time series. Econometric models retain their value as a reliable and interpretable tool for analyzing stable linear relationships. The results obtained confirm that the use of LSTM models with opti-mized parameters can significantly improve the accuracy of macroeconomic forecasts, which is an important condition for the formation of scientifically sound industrial and economic policy.