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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">finance</journal-id><journal-title-group><journal-title xml:lang="ru">Финансы: теория и практика/Finance: Theory and Practice</journal-title><trans-title-group xml:lang="en"><trans-title>Finance: Theory and Practice</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2587-5671</issn><issn pub-type="epub">2587-7089</issn><publisher><publisher-name>Financial University under The Government of Russian Federation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26794/2587-5671-2026-30-1-66-78</article-id><article-id custom-type="elpub" pub-id-type="custom">finance-4171</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ГОСУДАРСТВЕННЫЕ ФИНАНСЫ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>STATE FINANCES</subject></subj-group></article-categories><title-group><article-title>Новые подходы к прогнозированию доходов бюджетов Российской Федерации на основе резервуарных вычислений</article-title><trans-title-group xml:lang="en"><trans-title>New Approaches to Forecasting Budget Revenues of the Russian Federation Based on Reservoir Computing</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5120-7816</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Караев</surname><given-names>А. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Karaev</surname><given-names>A. K.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алан Канаматович Караев – доктор экономических наук, профессор, главный научный сотрудник Института исследований социально-экономических трансформаций и финансовой политики</p><p>Москва</p></bio><bio xml:lang="en"><p>Alan K. Karaev – Dr. Sci. (Econ.), Prof., Chief Researcher at the Institute for Research on Socio-Economic Transformations and Financial Policy</p><p>Moscow</p></bio><email xlink:type="simple">akkaraev@fa.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0005-2398-8159</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бельников</surname><given-names>С. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Belnikov</surname><given-names>S. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сергей Сергеевич Бельников – младший научный сотрудник Института исследований социально-экономических трансформаций и финансовой политики</p><p>Москва</p></bio><bio xml:lang="en"><p>Sergey S. Belnikov – Junior Researcher at the Institute for Research on Socio-Economic Transformations and Financial Policy</p><p>Moscow</p></bio><email xlink:type="simple">ssbelnikov@fa.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7889-2745</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Борисова</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Borisova</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ольга Викторовна Борисова – кандидат экономических наук, доцент, доцент кафедрыкорпоративных финансов и корпоративного управления факультета экономики и бизнеса</p><p>Москва</p></bio><bio xml:lang="en"><p>Olga V. Borisova – Cand. Sci. (Econ.), Assoc. Prof., Assoc. Prof. of the Department of Corporate Finance and Corporate Governance</p><p>Moscow</p></bio><email xlink:type="simple">olvborisova@fa.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Финансовый университет при Правительстве Российской Федерации</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Financial University under the Government of the Russian Federation</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>22</day><month>02</month><year>2026</year></pub-date><volume>30</volume><issue>1</issue><fpage>66</fpage><lpage>78</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Караев А.К., Бельников С.С., Борисова О.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Караев А.К., Бельников С.С., Борисова О.В.</copyright-holder><copyright-holder xml:lang="en">Karaev A.K., Belnikov S.S., Borisova O.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://financetp.fa.ru/jour/article/view/4171">https://financetp.fa.ru/jour/article/view/4171</self-uri><abstract><p>Актуальность исследования обусловлена необходимостью повышения точности прогностического инструментария при определении будущих доходов бюджета Российской Федерации в условиях динамичности макроэкономической ситуации, связанной с санкционными ограничениями. В сложившейся ситуации необходима оперативная реакция на происходящие изменения, что стимулирует использование данных различной периодичности в прогностических моделях и поиск новых более точных методов прогнозирования.</p><p>Объектом исследования является динамика доходов федерального бюджета.</p><p>Предмет исследования – применимость резервуарных вычислений для прогнозирования доходов федерального бюджета Российской Федерации.</p><p>Цель исследования заключается в выявлении целесообразности использования моделей резервуарных вычислений при прогнозировании доходов федерального бюджета Российской Федерации. В процессе исследования применялись эмпирические и теоретические методы. Они позволили описать суть резервуарных вычислений, пояснить полученные прогностические результаты и выбрать наиболее оптимальные гиперпараметры. В результате была предложена авторская модель на базе резервуарных вычислений, учитывающая динамику ежемесячных и ежедневных факторов развития российской экономики. Сделан вывод о том, что первый в мире опыт использования резервуарных вычислений при прогнозировании доходов федерального бюджета Российской Федерации позволил повысить качество модели. Характеристики полученной модели существенно лучше аналогов, рассчитанных с использованием иных методов. Также выявлена высокая фрагментарность российских данных и короткая длина временных рядов, что было устранено за счет сокращения временного периода для обучения моделей и импутации отсутствующих значений в данных.</p></abstract><trans-abstract xml:lang="en"><p>The relevance of this study stems from the need to enhance the accuracy of forecasting tools in determining future budget revenues for the Russian Federation, given the dynamic macroeconomic environment shaped by sanctions. In the current situation, it is essential to respond quickly to the changes taking place. This requires the use of various frequency data in predictive models and the search for new, more accurate forecasting methods. The object of the study is the dynamics of federal budget revenues. The subject of the research is to examine the applicability of reservoir computing in forecasting federal budget revenues in the Russian Federation. The purpose of the study is to identify the feasibility of using reservoir computing models in forecasting federal budget revenues in the Russian Federation. Empirical and theoretical methods were employed in the research process. These methods allowed us to understand the essence of reservoir computing, interpret the predictive results obtained, and select the best hyperparameters. As a result, a model based on reservoir computing was proposed by the author, taking into account the dynamics of monthly and daily factors in the development of the Russian economy. It is concluded that the world’s first experience in using reservoir computing in forecasting federal budget revenues in the Russian Federation has improved the quality of the model. The characteristics of the resulting model are significantly better than analogues calculated using other methods. The high fragmentation of the Russian data and the short length of the time series have also been revealed, which was eliminated by shortening the time period for training models and imputing missing values in the data.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>прогнозирование доходов федерального бюджета</kwd><kwd>резервуарные вычисления</kwd><kwd>машинное обучение</kwd><kwd>предобработка данных</kwd><kwd>PCA</kwd></kwd-group><kwd-group xml:lang="en"><kwd>federal budget revenue forecasting</kwd><kwd>reservoir computing</kwd><kwd>machine learning</kwd><kwd>data preprocessing</kwd><kwd>PCA</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Статья подготовлена по результатам исследований, выполненных за счет бюджетных средств по государственному заданию Финуниверситету. Финансовый университет при Правительстве Российской Федерации, Москва, Российская Федерация.</funding-statement><funding-statement xml:lang="en">The article was prepared based on the results of research carried out at the expense of budgetary funds according to the state assignment of the Financial University. Financial University under the Government of the Russian Federation, Moscow, Russian Federation.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Glenday G. Revenue forecasting. In: Allen R., Hemming R., Potter B. H., eds. The international handbook of public financial management. London: Palgrave Macmillan; 2013:435-452. DOI: https://doi.org/10.1057/9781137315304_21</mixed-citation><mixed-citation xml:lang="en">Glenday G. Revenue forecasting. In: Allen R., Hemming R., Potter B. H., eds. The international handbook of public financial management. London: Palgrave Macmillan; 2013:435-452. DOI: https://doi.org/10.1057/9781137315304_21</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Noor N., Sarlan A., Aziz N. Government revenue prediction using feed forward neural network. Journal of Theoretical and Applied Information Technology. 2023;101(6):2459-2473.</mixed-citation><mixed-citation xml:lang="en">Noor N., Sarlan A., Aziz N. Government revenue prediction using feed forward neural network. Journal of Theoretical and Applied Information Technology. 2023;101(6):2459-2473.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Batóg B., Batóg J. Regional government revenue forecasting: Risk factors of investment financing. Risks. 2021;9(12):210. DOI: 10.3390/risks9120210</mixed-citation><mixed-citation xml:lang="en">Batóg B., Batóg J. Regional government revenue forecasting: Risk factors of investment financing. Risks. 2021;9(12):210. DOI: 10.3390/risks9120210</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Серков Л. А. Критический подход к анализу проблем динамических стохастических моделей общего равновесия. Экономика и бизнес: теория и практика. 2015;(8):122-126.</mixed-citation><mixed-citation xml:lang="en">Serkov L. A. Critical approach to the analysis of the problems of dynamic stochastic general equilibrium model. Ekonomika i biznes: teoriya i praktika = Economy and Business: Theory and Practice. 2015;(8):122-126. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Storm S. Cordon of conformity: Why DSGE models are not the future of macroeconomics. International Journal of Political Economy. 2021;50(2):77-98. DOI: 10.1080/08911916.2021.1929582</mixed-citation><mixed-citation xml:lang="en">Storm S. Cordon of conformity: Why DSGE models are not the future of macroeconomics. International Journal of Political Economy. 2021;50(2):77-98. DOI: 10.1080/08911916.2021.1929582</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Abdi G., Mazur T., Szaciłowski K. An organized view of reservoir computing: A perspective on theory and technology development. Japanese Journal of Applied Physics. 2024;63(5):050803. DOI: 10.35848/1347-4065/ad394f</mixed-citation><mixed-citation xml:lang="en">Abdi G., Mazur T., Szaciłowski K. An organized view of reservoir computing: A perspective on theory and technology development. Japanese Journal of Applied Physics. 2024;63(5):050803. DOI: 10.35848/1347-4065/ad394f</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Караев А. К., Борисова О. В. Перспективные модели финансового прогнозирования доходов бюджета. Финансы: теория и практика. 2025;29(1):20-33. DOI: 10.26794/2587-5671-2025-29-1-20-33</mixed-citation><mixed-citation xml:lang="en">Karaev A. K., Borisova O. V. Prospective models of financial forecasting of budget revenues. Finance: Theory and Practice. 2025;29(1):20-33. DOI: 10.26794/2587-5671-2025-29-1-20-33</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Ballarin G., et al. Reservoir computing for macroeconomic forecasting with mixed-frequency data. International Journal of Forecasting. 2024;40(3):1206-1237. DOI: 10.1016/j.ijforecast.2023.10.009</mixed-citation><mixed-citation xml:lang="en">Ballarin G., et al. Reservoir computing for macroeconomic forecasting with mixed-frequency data. International Journal of Forecasting. 2024;40(3):1206-1237. DOI: 10.1016/j.ijforecast.2023.10.009</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Santos A., Lima R. R., Alves J. L., Misturini D. W., Florindo J. B. Reservoir computing and non-linear dynamics for time series analysis: An application in the financial market. Physica D: Nonlinear Phenomena. 2025;476:134698. DOI: 10.1016/j.physd.2025.134698</mixed-citation><mixed-citation xml:lang="en">Santos A., Lima R. R., Alves J. L., Misturini D. W., Florindo J. B. Reservoir computing and non-linear dynamics for time series analysis: An application in the financial market. Physica D: Nonlinear Phenomena. 2025;476:134698. DOI: 10.1016/j.physd.2025.134698</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Jaeger H. The “echo state” approach to analysing and training recurrent neural networks — with an erratum note. German National Research Center for Information Technology. GMD Report. 2001;(148). URL: https://www.researchgate.net/publication/215385037_The_echo_state_approach_to_analysing_and_training_recurrent_neural_networks-with_an_erratum_note’</mixed-citation><mixed-citation xml:lang="en">Jaeger H. The “echo state” approach to analysing and training recurrent neural networks — with an erratum note. German National Research Center for Information Technology. GMD Report. 2001;(148). URL: https://www.researchgate.net/publication/215385037_The_echo_state_approach_to_analysing_and_training_recurrent_neural_networks-with_an_erratum_note’</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Jaeger H., Haas H. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science. 2004;304(5667):78-80. DOI: 10.1126/science.1091277</mixed-citation><mixed-citation xml:lang="en">Jaeger H., Haas H. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science. 2004;304(5667):78-80. DOI: 10.1126/science.1091277</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Pathak J., et al. Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Physical Review Letters. 2018;120:024102. DOI: 10.1103/PhysRev-Lett.120.024102</mixed-citation><mixed-citation xml:lang="en">Pathak J., et al. Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Physical Review Letters. 2018;120:024102. DOI: 10.1103/PhysRevLett.120.024102</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Gauthier D. J. et al. Next generation reservoir computing. Nature Communications. 2021;12:5564. DOI: 10.1038/s41467-021-25801-2</mixed-citation><mixed-citation xml:lang="en">Gauthier D. J., et al. Next generation reservoir computing. Nature Communications. 2021;12:5564. DOI: 10.1038/s41467-021-25801-2</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Platt J. A., Wong A., Clark R., Penny S. G., Abarbanel H. D.I. Forecasting using reservoir computing: The role of generalized synchronization. arXiv preprint. 2021. DOI: 10.48550/arXiv.2103.00362</mixed-citation><mixed-citation xml:lang="en">Platt J. A., Wong A., Clark R., Penny S. G., Abarbanel H. D.I. Forecasting using reservoir computing: The role of generalized synchronization. arXiv preprint. 2021. DOI: 10.48550/arXiv.2103.00362</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Tziatzios P. Financial nonlinear time-series analysis and prediction with reservoir computing. Master of science thesis in data science. School of Science &amp; Technology. 2019.</mixed-citation><mixed-citation xml:lang="en">Tziatzios P. Financial nonlinear time-series analysis and prediction with reservoir computing. Master of science thesis in data science. School of Science &amp; Technology. 2019.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Bollt E. M. On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2021;31(1):013108. DOI: 10.1063/5.0024890</mixed-citation><mixed-citation xml:lang="en">Bollt E. M. On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2021;31(1):013108. DOI: 10.1063/5.0024890</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Борисова О. В. Отдельные аспекты финансового прогнозирования в государственном секторе. РИСК: Ресурсы, Информация, Снабжение, Конкуренция. 2023;(2):177-181. DOI: 10.56584/1560-8816-2023-2-177-181</mixed-citation><mixed-citation xml:lang="en">Borisova O. V. Separate aspects of financial forecasting in the public sector. RISK: resursy, informatsiya, snabzhenie, konkurentsiya = RISK: Resources, Information, Supply, Competition. 2023;(2):177-181. (In Russ.). DOI: 10.56584/1560-8816-2023-2-177-181</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Караев А. К., Понкратов В. В. Основы балансовой механики Вольфганга Штютцела. Мир новой экономики. 2018;12(1):104-113. DOI: 10.26794/2220-6469-2018-12-1-104-113</mixed-citation><mixed-citation xml:lang="en">Karaev A. K., Ponkratov V. V. Basics of the Wolfgang Stützel’s balance mechanics. Mir novoi ekonomiki = The World of New Economy. 2018;12(1):104-113. (In Russ.). DOI: 10.26794/2220-6469-2018-12-1-104-113</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Караев А. К., Понкратов В. В. Взаимосвязь финансового развития и экономического роста России (2000-2022 годы). Экономика. Налоги. Право. 2024;17(2):17-26. DOI: 10.26794/1999-849X-2024-17-2-17-26</mixed-citation><mixed-citation xml:lang="en">Karaev A. K., Ponkratov V. V. The relationship between financial development and economic growth in Russia (2000-2022). Ekonomika. Nalogi. Pravo = Economics, Taxes &amp; Law. 2024;17(2):17-26. (In Russ.). DOI: 10.26794/1999-849X-2024-17-2-17-26</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
