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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">ecpolicy</journal-id><journal-title-group><journal-title xml:lang="ru">Экономическая политика</journal-title><trans-title-group xml:lang="en"><trans-title>Economic Policy</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1994-5124</issn><issn pub-type="epub">2411-2658</issn><publisher><publisher-name>Economic Policy</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.18288/1994-5124-2026-2-32-65</article-id><article-id custom-type="elpub" pub-id-type="custom">ecpolicy-661</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>Региональная экономика</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Regional Economy</subject></subj-group></article-categories><title-group><article-title>Кластеризация регионов России на основе данных наличного денежного обращения</article-title><trans-title-group xml:lang="en"><trans-title>Clustering Russian Regions by Cash Circulation</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2653-1745</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шайдуллин</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Shaidullin</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ансэль Ильгизович Шайдуллин – главный экономист отдела мониторинга и исследования данных управления развития и аналитики наличного денежного обращения департамента наличного денежного обращения, Банк России; аспирант, Национальный   исследовательский университет «Высшая школа экономики»</p><p>125040, Москва, ул. Правды, 6, стр. 2; 101000, Москва, Мясницкая ул., 20</p></bio><bio xml:lang="en"><p>Ansel I. Shaidullin, Chief Economist, Monitoring and Data Research Section, Division of Cash Circulation Development and Analysis, Departmen of Cash Circulation, Bank of Russia;  Postgraduate Student, HSE University</p><p>6–2, Pravdy ul., Moscow, 125040: 20, Myasnitskaya ul., Moscow, 101000</p><p> </p></bio><email xlink:type="simple">ansel.shajdullin@yandex.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/0000-0001-7591-8340</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Седипкова</surname><given-names>С. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Sedipkova</surname><given-names>S. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Снежана Владимировна Седипкова – ведущий экономист отдела анализа наличного денежного обращения и организации работы с резервными фондами банкнот и монеты Центра организации наличного денежного обращения и операционного обслуживания </p><p>630099, Новосибирск, Красный пр., 27</p><p> </p></bio><bio xml:lang="en"><p>Snezhana V. Sedipkova, Lead Economist, Cash Circulation Analysis Section, Cash Circulation Division </p><p>27, Krasnyy pr., Novosibirsk, 630099</p><p> </p></bio><email xlink:type="simple">snezhana.nsk@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Банк России; &#13;
Национальный   исследовательский университет «Высшая школа экономики»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Bank of Russia; &#13;
HSE University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Сибирское ГУ Банка России</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian Main Branch of the Bank of Russia</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>20</day><month>04</month><year>2026</year></pub-date><volume>21</volume><issue>2</issue><fpage>32</fpage><lpage>65</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шайдуллин А.И., Седипкова С.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Шайдуллин А.И., Седипкова С.В.</copyright-holder><copyright-holder xml:lang="en">Shaidullin A.I., Sedipkova S.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://www.ecpolicy.ru/jour/article/view/661">https://www.ecpolicy.ru/jour/article/view/661</self-uri><abstract><p>В периоды кризисов спрос на наличные деньги возрастает, увеличивая нагрузку на платежную инфраструктуру. Кластеризация регионов РФ позволит разработать дифференцированные сценарии реагирования на шоки и усовершенствовать прогнозный инструментарий с учетом региональной специфики. В статье представлена кластеризация регионов России на основе динамики приходно-расходных операций с наличными деньгами. С использованием корреляционно-кластерного анализа, метода Варда и алгоритма k-средних авторами выявлены группы субъектов РФ со схожими паттернами денежного обращения. На основе «метода локтя» определено, что для большинства номиналов оптимальным является разделение на три кластера, при этом границы групп варьируются в зависимости от волатильности операций. По наиболее часто встречающимся номиналам в обращении — 5000, 1000 и 500 руб. — в большинстве регионов РФ наблюдается схожая динамика приходно-расходных операций. Получен вывод о том, что в условиях значительных экзогенных шоков региональные паттерны использования наличных денег различных номиналов склонны к унификации. Формирование доминирующих кластеров свидетельствует о преобладании общенациональных факторов (изменение потребительского поведения, адаптация к неопределенности, единые меры экономической политики) над региональной спецификой в динамике наличного денежного обращения. Результаты исследования представляют практическую ценность для Банка России и других финансовых институтов, поскольку позволяют перейти к территориально ориентированным моделям прогнозирования спроса на наличность, что открывает возможности для оптимизации логистических процессов и минимизации издержек. Кроме того, предложенная методика может быть адаптирована для анализа других макроэкономических показателей, что расширяет сферу ее потенциального применения.</p></abstract><trans-abstract xml:lang="en"><p>Demand for cash increases during crises and thus places additional strain on the payment infrastructure. Clustering the regions of the Russian Federation will facilitate differentiated response scenarios to shocks and improve forecasting tools that are responsive to specific regional characteristics. This article clusters Russian regions on the basis of the dynamics of their cash inflows and outflows. By applying correlation clustering analysis, Ward s method, and the K-Means algorithm, the authors identified groups of Russia s constituent regions with similar cash circulation patterns. For most denominations, the Elbow Method resulted in an optimal division into three clusters, whose boundaries varied with the volatility of operations. Most Russian regions exhibit similar dynamics in cash transactions for the most common denominations in circulation (5,000, 1,000, and 500 rubles). Major exogenous shocks tend to make regional patterns in the use of various cash denominations uniform. The formation of dominant clusters indicates that nationwide factors (such as changes in consumer behavior, adaptation to uncertainty, and unified economic policies) prevail over regional specifics in the dynamics of cash circulation. The results of the study have practical applications for the Bank of Russia and other financial institutions in their effort to transition to territorially oriented forecasting of cash demand with consequent opportunities to optimize logistical processes and minimize costs. The methodology proposed by the authors potentially has a broader scope, as it can be adapted to analyze other macroeconomic indicators.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Банк России</kwd><kwd>корреляционно-кластерный анализ</kwd><kwd>«метод локтя»</kwd><kwd>метод k-средних</kwd><kwd>иерархическая кластеризация</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Bank of Russia</kwd><kwd>correlation clustering analysis</kwd><kwd>elbow method</kwd><kwd>K-Means method</kwd><kwd>hierarchical clustering</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Артемова М., Мамедли М., Синяков А. Кредитование домохозяйств в разрезе федеральных округов по данным опроса финансов домохозяйств: региональные особенности и потенциальные риски. Аналитическая записка. М.: Банк России, 2018. https://cbr.ru/content/document/file/48364/analytic_note_181004_dip.pdf.</mixed-citation><mixed-citation xml:lang="en">Artemova M., Mamedli M., Sinyakov A. Kreditovanie domokhozyaystv v razreze federal’nykh okrugov po dannym oprosa finansov domokhozyaystv: regional’nye osobennosti i potentsial’nye riski. Analiticheskaya zapiska [Household Lending Across Federal Districts According to Household Finance Survey Data: Regional Specificities and Potential Risks. Analytical Note]. Moscow, Bank of Russia, 2018. https://cbr.ru/content/document/file/48364/analytic_note_181004_dip.pdf. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Белов С. В., Карепов О. В. Вопросы обеспечения наличного денежного оборота на территории Дальневосточного федерального округа // Деньги и кредит. 2017. № 1. С. 53–56.</mixed-citation><mixed-citation xml:lang="en">Belov S. V., Karepov O. V. Voprosy obespecheniya nalichnogo denezhnogo oborota na territorii Dal’nevostochnogo federal’nogo okruga [Issues of Ensuring Cash Circulation Within the Far Eastern Federal District]. Den’gi i kredit [Russian Journal of Money &amp; Finance], 2017, no. 1, pp. 53-56. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Боголюбова Н. П., Никитин М. В. Региональная специфика взаимосвязей потребления домашних хозяйств и экономического развития в современной России // Вестник Алтайской академии экономики и права. 2019. № 4. С. 19–29.</mixed-citation><mixed-citation xml:lang="en">Bogolyubova N. P., Nikitin M. V. Regional’naya spetsifika vzaimosvyazey potrebleniya domashnikh khozyaystv i ekonomicheskogo razvitiya v sovremennoy Rossii [Regional Specificity of the Relationships of Household Consumption and Economic Development in Modern Russia]. Vestnik Altayskoy akademii ekonomiki i prava [Bulletin of the Altai Academy of Economics and Law], 2019, no. 4, pp. 19-29. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Губарев Р. В., Дзюба Е. И., Куликова О. М., Файзуллин Ф. С. Управление качеством жизни населения в регионах России // Журнал институциональных исследований. 2019. Т. 11. № 2. С. 146–170. DOI: 10.17835/2076-6297.2019.11.2.146-170.</mixed-citation><mixed-citation xml:lang="en">Gubarev R. V., Dzyuba E. I., Kulikova O. M., Fayzullin F. S. Upravlenie kachestvom zhizni naseleniya v regionakh Rossii [Quality Management of the Population in the Regions of Russia]. Zhurnal institutsional’nykh issledovaniy [Journal of Institutional Studies], 2019, vol. 11, no. 2, pp. 146-170. DOI: 10.17835/2076-6297.2019.11.2.146-170. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Заварухин В. П., Чинаева И., Чурилова Э. Ю. Регионы России: результаты кластеризации на основе экономических и инновационных показателей // Статистика и экономика. 2022. Т. 19. № 5. С. 35–47. DOI: 10.21686/2500-3925-2022-5-35-47.</mixed-citation><mixed-citation xml:lang="en">Zavarukhin V. P., Chinaeva I., Churilova E. Yu. Regiony Rossii: rezul’taty klasterizatsii na osnove ekonomicheskikh i innovatsionnykh pokazateley [Regions of Russia: Clustering Results Based on Economic and Innovation Indexes]. Statistika i ekonomika [Statistics and Economics], 2022, vol. 19, no. 5, pp. 35-47. DOI: 10.21686/2500-3925-2022-5-35-47. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Ильясов Б. Г., Макарова Е. А., Закиева Е. Ш., Гиздатуллина Э. С. Оценка данных о доходах населения в региональном разрезе методом главных компонент // Экономика региона. 2019. Т. 15. № 2. С. 601–617. DOI: 10.17059/2019-2-22.</mixed-citation><mixed-citation xml:lang="en">Ilyasov B. G., Makarova E. A., Zakieva E. Sh., Gizdatullina E. S. Otsenka dannykh o dokhodakh naseleniya v regional’nom razreze metodom glavnykh komponent [Analyzing the Data on Incomes in the Regional Context by the Principal Component Method]. Ekonomika regiona [Economy of Regions], 2019, vol. 15, no. 2, pp. 601-617. DOI: 10.17059/2019-2-22. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ионов В. М. О месте и роли наличных денег в мировой экономике (Исчезнут ли наличные деньги?) // Деньги и кредит. 2016. № 10. С. 43–50.</mixed-citation><mixed-citation xml:lang="en">Ionov V. M. O meste i roli nalichnykh deneg v mirovoy ekonomike (Ischeznut li nalichnye den’gi?) [On the Role and Place of Cash in Global Economy (Will Cash Disappear?)]. Den’gi i kredit [Russian Journal of Money &amp; Finance], 2016, no. 10, pp. 43-50. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Кетова К. В., Касаткина Е. В., Вавилова Д. Д. Кластеризация регионов Российской Федерации по уровню социально-экономического развития с использованием методов машинного обучения // Экономические и социальные перемены: факты, тенденции, прогноз. 2021. Т. 14. № 6. С. 70–85. DOI: 10.15838/esc.2021.6.78.4.</mixed-citation><mixed-citation xml:lang="en">Ketova K. V., Kasatkina E. V., Vavilova D. D. Klasterizatsiya regionov Rossiyskoy Federatsii po urovnyu sotsial’no-ekonomicheskogo razvitiya s ispol’zovaniem metodov mashinnogo obucheniya [Clustering Russian Federation Regions According to the Level of SocioEconomic Development With the Use of Machine Learning Methods]. Ekonomicheskie i sotsial’nye peremeny: fakty, tendentsii, prognoz [Economic and Social Changes: Facts, Trends, Forecast], 2021, vol. 14, no. 6, pp. 70-85. DOI: 10.15838/esc.2021.6.78.4. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Криворучко С. В. Спрос на деньги и обращение банкнот крупных номиналов: современные тенденции // Финансовый журнал. 2019. № 2. С. 96–108. DOI: 10.31107/2075-1990-2019-2-96-108.</mixed-citation><mixed-citation xml:lang="en">Krivoruchko S. V. Spros na den’gi i obrashchenie banknot krupnykh nominalov: sovremennye tendentsii [Demand for Money and Circulation of High Denomination Notes: Current Trend]. Finansovyy zhurnal [Financial Journal], 2019, no. 2, pp. 96-108. DOI: 10.31107/2075-1990-2019-2-96-108. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Отношение населения Российской Федерации к различным средствам платежа: результаты социологического исследования за 2023 год. М.: Банк России, 2023. https://cbr.ru/Collection/Collection/File/49252/results_2023.pdf.</mixed-citation><mixed-citation xml:lang="en">Otnoshenie naseleniya Rossiyskoy Federatsii k razlichnym sredstvam platezha: rezul’taty sotsiologicheskogo issledovaniya za 2023 god [Russian Population Attitudes Towards Different Payment Instruments: Results of Sociological Study for 2023]. Moscow, Bank of Russia, 2023. https://cbr.ru/Collection/Collection/File/49252/results_2023.pdf. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Пискун Е. И., Хохлов В. В. Экономическое развитие регионов Российской Федерации. Факторно-кластерный анализ // Экономика региона. 2019. Т. 15. № 2. С. 363–376. DOI: 10.17059/2019-2-5.</mixed-citation><mixed-citation xml:lang="en">Piskun E. I., Khokhlov V. V. Ekonomicheskoe razvitie regionov Rossiyskoy Federatsii. Faktorno-klasternyy analiz [Economic Development of the Russian Federation’s Regions: Factor-Cluster Analysis]. Ekonomika regiona [Economy of Regions], 2019, vol. 15, no. 2, pp. 363-376. DOI: 10.17059/2019-2-5. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Протасов Ю. М., Юров В. М. Кластеризация регионов РФ по уровню их социально-экономического развития // Вестник Московского государственного областного университета. Серия: Экономика. 2022. № 2. С. 95–103. DOI: 10.18384/2310-6646-2022-2-95-103.</mixed-citation><mixed-citation xml:lang="en">Protasov Yu. M., Yurov V. M. Klasterizatsiya regionov RF po urovnyu ikh sotsial’no-ekonomicheskogo razvitiya [Clusterization of the Regions of the Russian Federation by Their Level of Socio-Economic Development]. Vestnik Moskovskogo gosudarstvennogo oblastnogo universiteta. Seriya: Ekonomika [Bulletin of the Moscow State University of Education. Series: Economics], 2022, no. 2, pp. 95-103. DOI: 10.18384/2310-6646-2022-2-95-103. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Развитие и регулирование рынка инкассации и перевозки наличных денег: доклад для общественных консультаций. М.: Банк России, 2024. https://cbr.ru/Content/Document/File/165616/Consultation_Paper_30082024.pdf.</mixed-citation><mixed-citation xml:lang="en">Razvitie i regulirovanie rynka inkassatsii i perevozki nalichnykh deneg: doklad dlya obshchestvennykh konsul’tatsiy [Development and Regulation of Cash-In-Transit Market: Consultation Paper]. Moscow, Bank of Russia, 2024. https://cbr.ru/Content/Document/File/165616/Consultation_Paper_30082024.pdf. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Структура наличной денежной массы в обращении. М.: Банк России, 2025. http://cbr.ru/statistics/cash_circulation/20250401.</mixed-citation><mixed-citation xml:lang="en">Struktura nalichnoy denezhnoy massy v obrashchenii [Structure of Cash Money Supply in Circulation]. Moscow, Bank of Russia, 2025. http://cbr.ru/statistics/cash_circulation/20250401. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Четверикова Е., Гудкова Ю., Воронцова А., Манухина Ю. Гетерогенность сберегательной активности регионов России, ее предикторов и детерминант. Банк Росии. Серия докладов об экономических исследованиях. № 101. 2022. https://cbr.ru/StaticHtml/File/142779/wp_101.pdf.</mixed-citation><mixed-citation xml:lang="en">Chetverikova E., Gudkova Yu., Vorontsova A., Manukhina Yu. Geterogennost’ sberegatel’noy aktivnosti regionov Rossii, ee prediktorov i determinant [Heterogeneity of Saving Activity in Russian Regions, Its Predictors and Determinants]. Bank of Russia: Economic Research Report Series, no. 101, 2022. https://cbr.ru/StaticHtml/File/142779/wp_101.pdf. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Adolfsson А., Ackerman М., Brownstein N. C. To Cluster, or Not to Cluster: An Analysis of Clusterability Methods // Pattern Recognition. 2018. P. 1–18. DOI: 10.1016/j.patcog.2018.10.026.</mixed-citation><mixed-citation xml:lang="en">Adolfsson A., Ackerman M., Brownstein N. C. To Cluster, or Not to Cluster: An Analysis of Clusterability Methods. Pattern Recognition, 2018, pp. 1-18. DOI: 10.1016/j.patcog.2018.10.026.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Community Access to Cash Pilots: Final Report. London: Cash Access UK Limited, 2021. https://www.toynbeehall.org.uk/wp-content/uploads/2021/12/CACP_Report_FINAL-for-sharing.pdf.</mixed-citation><mixed-citation xml:lang="en">Community Access to Cash Pilots: Final Report. London, Cash Access UK Limited, 2021. https://www.toynbeehall.org.uk/wp-content/uploads/2021/12/CACP_Report_FINAL-for-sharing.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Consultation on the Bank of England’s Supervisory Approach to Wholesale Cash Distribution. London: Bank of England, 2022. https://www.bankofengland.co.uk/paper/2022/consultation-on-the-bank-of-englands-supervisory-approach-to-wholesalecash-distribution.</mixed-citation><mixed-citation xml:lang="en">Consultation on the Bank of England’s Supervisory Approach to Wholesale Cash Distribution. London, Bank of England, 2022. https://www.bankofengland.co.uk/paper/2022/consultation-on-the-bank-of-englands-supervisory-approach-to-wholesale-cash-distribution.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Bartzsch N., Rösl G., Seitz F. The Circulation of German Euro Banknotes Abroad: Estimates Applying Direct Methods. Deutsche Bundesbank. Discussion Paper. Series 1. No 20. 2011a.</mixed-citation><mixed-citation xml:lang="en">Bartzsch N., Rösl G., Seitz F. The Circulation of German Euro Banknotes Abroad: Estimates Applying Direct Methods. Deutsche Bundesbank, Discussion Paper, series 1, no. 20, 2011a.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Bartzsch N., Rösl G., Seitz F. The Circulation of German Euro Banknotes Abroad: Estimates Applying Indirect Methods. Deutsche Bundesbank. Discussion Paper. Series 1. No 21. 2011b.</mixed-citation><mixed-citation xml:lang="en">Bartzsch N., Rösl G., Seitz F. The Circulation of German Euro Banknotes Abroad: Estimates Applying Indirect Methods. Deutsche Bundesbank, Discussion Paper, series 1, no. 21, 2011b.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Brown J. R., Gustafson M. T., Ivanov I. T. Weathering Cash Flow Shocks // The Journal of Finance. 2021. Vol. 76. Iss. 4. P. 1731–1772.</mixed-citation><mixed-citation xml:lang="en">Brown J. R., Gustafson M. T., Ivanov I. T. Weathering Cash Flow Shocks. The Journal of Finance, 2021, vol. 76, no. 4, pp. 1731-1772.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Chen H., Engert W., Huynh K. P., Nicholls G., Nicholson M., Zhu J. Cash and COVID-19: The Impact of the Pandemic on the Demand for and Use of Cash. Bank of Canada. Staff Discussion Paper. No 2020-6. 2020. DOI: 10.34989/sdp-2020-6.</mixed-citation><mixed-citation xml:lang="en">Chen H., Engert W., Huynh K. P., Nicholls G., Nicholson M., Zhu J. Cash and COVID-19: The Impact of Pandemic on Demand for and Use of Cash. Bank of Canada, Staff Discussion Paper, no. 2020-6, 2020. DOI: 10.34989/sdp-2020-6.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Cui M. Introduction to the K-Means Clustering Algorithm Based on the Elbow Method // Accounting, Auditing and Finance. 2020. Vol. 1. Iss. 1. P. 5–8.</mixed-citation><mixed-citation xml:lang="en">Cui M. Introduction to the K-Means Clustering Algorithm Based on the Elbow Method. Accounting, Auditing and Finance, 2020, vol. 1, no. 1, pp. 5-8.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Dias A. Estimating a Country’s Currency Circulation Within a Monetary Union // Ninth IFC Conference on Are Post-Crisis Statistical Initiatives Completed? Basel: Bank of Portugal, 2018.</mixed-citation><mixed-citation xml:lang="en">Dias A. Estimating a Country’s Currency Circulation Within a Monetary Union. In: Ninth IFC Conference on Are Post-Crisis Statistical Initiatives Completed? Basel, Bank of Portugal, 2018.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Enright M. J. Survey on the Characterization of Regional Clusters: Initial Results. Hong Kong: Institute of Economic Policy and Business Strategy; The Competitiveness Institute, 2000.</mixed-citation><mixed-citation xml:lang="en">Enright M. J. Survey on the Characterization of Regional Clusters: Initial Results. Hong Kong, Institute of Economic Policy and Business Strategy, The Competitiveness Institute, 2000.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Study on the Payment Attitudes of Consumers in the Euro Area. Frankfurt on the Main: European Central Bank, 2022. https://www.ecb.europa.eu/stats/ecb_surveys/space/html/ecb.space2024~19d46f0f17.en.html.</mixed-citation><mixed-citation xml:lang="en">Study on the Payment Attitudes of Consumers in the Euro Area. Frankfurt on the Main, European Central Bank, 2022. https://www.ecb.europa.eu/stats/ecb_surveys/space/html/ecb.space2024~19d46f0f17.en.html.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Ghosal A., Nandy A., Das A. K., Goswami S., Panday M. A Short Review on Different Clustering Techniques and Their Applications. Emerging Technology in Modelling and Graphics // Advances in Intelligent Systems and Computing. Singapore: Springer, 2022. Vol. 937. P. 69–83. DOI: 10.1007/978-981-13-7403-6_9.</mixed-citation><mixed-citation xml:lang="en">Ghosal A., Nandy A., Das A. K., Goswami S., Panday M. A. A Short Review on Different Clustering Techniques and Their Applications. Emerging Technology in Modelling and Graphics: Proceedings of IEM Graph, 2020, pp. 69-83.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Hesananda R., Apriliga P. Customer Segmentation of Cash Management System Using K-Means Clustering // Journal of Applied and Research Computer Science and Information Systems. 2024. Vol. 2. Iss. 2. P. 191–202.</mixed-citation><mixed-citation xml:lang="en">Hesananda R., Apriliga P. Customer Segmentation of Cash Management System Using K-Means Clustering. Journal of Applied and Research Computer Science and Information Systems, 2024, vol. 2, no. 2, pp. 191-202.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Kleinberg J. An Impossibility Theorem for Clustering // Proceedings of the 15th International Conference on Neural Information Processing Systems. Vancouver, 9–14 December 2002. Cambridge, MA: MIT Press, 2002. P. 463–470.</mixed-citation><mixed-citation xml:lang="en">Kleinberg J. An Impossibility Theorem for Clustering. In: Proceedings of the 15th International Conference on Neural Information Processing Systems. Vancouver, 9-14 December 2002. Cambridge, MA, MIT Press, 2002, pp. 463-470.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Liu F., Deng Y. Determine the Number of Unknown Targets in Open World Based on Elbow Method // IEEE Transactions on Fuzzy Systems. 2021. Vol. 29. Iss. 5. P. 986–995. DOI: 10.1109/tfuzz.2020.2966182.</mixed-citation><mixed-citation xml:lang="en">Liu F., Deng Y. Determine the Number of Unknown Targets in Open World Based on Elbow Method. IEEE Transactions on Fuzzy Systems, 2021, vol. 29, no. 5, pp. 986-995. DOI: 10.1109/tfuzz.2020.2966182.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Schubert E. Stop Using the Elbow Criterion for K-Means and How to Choose the Number of Clusters Instead // ACM SIGKDD Exploration Newsletter. 2023. Vol. 25. Iss. 1. P. 36–42. DOI: 10.1145/3606274.3606278.</mixed-citation><mixed-citation xml:lang="en">Schubert E. Stop Using the Elbow Criterion for K-Means and How to Choose the Number of Clusters Instead. ACM SIGKDD Exploration Newsletter, 2023, vol. 25, no. 1, pp. 36-42. DOI: 10.1145/3606274.3606278.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Shahapure K. R., Nicholas C. Cluster Quality Analysis Using Silhouette Score // 2020 IEEE 7th International Conference on Data Science and Advanced Analytics. Sydney, 6–9 October 2020. New York: IEEE, 2020. DOI: 10.1109/dsaa49011.2020.00096.</mixed-citation><mixed-citation xml:lang="en">Shahapure K. R., Nicholas C. Cluster Quality Analysis Using Silhouette Score. In: 2020 IEEE 7th International Conference on Data Science and Advanced Analytics. Sydney, 6-9 October 2020. New York, IEEE, 2020. DOI: 10.1109/dsaa49011.2020.00096.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Shirai S., Sugandi E. A. Growing Global Demand for Cash // International Business Research. 2019. Vol. 12. Iss. 12. P. 74. DOI: 10.5539/ibr.v12n12p74.</mixed-citation><mixed-citation xml:lang="en">Shirai S., Sugandi E. A. Growing Global Demand for Cash. International Business Research, 2019, vol. 12, no. 12, p. 74. DOI: 10.5539/ibr.v12n12p74.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Shutaywi M., Kachouie N. N. Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering // Entropy. 2021. Vol. 23. Iss. 6. Art. 759. P. 1–17. DOI: 10.3390/e23060759.</mixed-citation><mixed-citation xml:lang="en">Shutaywi M., Kachouie N. N. Silhouette Analysis for Performance Evaluation in Machine Learning With Applications to Clustering. Entropy, 2021, vol. 23, no. 6, pp. 1-17. DOI: 10.3390/e23060759.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Simutis R., Dilijonas D., Bastina L. Cash Demand Forecasting for ATM Using Neural Networks and Support Vector Regression Algorithms // Proceedings of the 20th EURO Mini Conference Continuous Optimization and Knowledge-Based Technologies. Neringa, 20–23 May 2008. Vilnius: Institute of Mathematics and Informatics; Vilnius Gediminas Technical University, 2008. P. 416–421.</mixed-citation><mixed-citation xml:lang="en">Simutis R., Dilijonas D., Bastina L. Cash Demand Forecasting for ATM Using Neural Networks and Support Vector Regression Algorithms. In: Proceedings of the 20th EURO Mini Conference Continuous Optimization and Knowledge-Based Technologies. Neringa, 2023 May, 2008. Vilnius, Institute of Mathematics and Informatics, Vilnius Gediminas Technical University, 2008, рр. 416-421.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Spaanderman J. The Role and Future of Cash // Occasional Studies. 2023. Vol. 18. Iss. 2. P. 1–52.</mixed-citation><mixed-citation xml:lang="en">Spaanderman J. The Role and Future of Cash. Occasional Studies, 2023, vol. 18, no. 2, pp. 1-52.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Syakur M. A., Khotimah B. K., Rochman E. M. S., Satoto B. D. Integration K-Means Clustering Method and Elbow Method for Identification of the Best Customer Profile Cluster // IOP Conference Series: Materials Science and Engineering. Surabaya, 9 November 2017. Bristol: IOP Publishing, 2018. Vol. 336. P. 1–7.</mixed-citation><mixed-citation xml:lang="en">Syakur M. A., Khotimah B. K., Rochman E. M. S., Satoto B. D. Integration K-Means Clustering Method and Elbow Method for Identification of Best Customer Profile Cluster. In: IOP Conference Series: Materials Science and Engineering. Surabaya, 9 November 2017. Bristol, IOP Publishing, 2018, vol. 336, pp. 1-7.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Thorndike R. L. Who Belongs in the Family? // Psychometrika. 1953. Vol. 18. Iss. 4. P. 267– 276. DOI: 10.1007/BF02289263.</mixed-citation><mixed-citation xml:lang="en">Thorndike R. L. Who Belongs in the Family? Psychometrika, 1953, vol. 18, no. 4, pp. 267276. DOI: 10.1007/BF02289263.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Vidyattama Y. Issues in Applying Spatial Autocorrelation on Indonesia’s Provincial Income Growth Analysis // Australasian Journal of Regional Studies. 2014. Vol. 20. Iss. 2. P. 375–402.</mixed-citation><mixed-citation xml:lang="en">Vidyattama Y. Issues in Applying Spatial Autocorrelation on Indonesia’s Provincial Income Growth Analysis. Australasian Journal of Regional Studies, 2014, vol. 20, no. 2, pp. 375-402.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Ward J. H. Hierarchical Grouping to Optimize an Objective Function // Journal of the American Statistical Association. 1963. Vol. 58. P. 236–244.</mixed-citation><mixed-citation xml:lang="en">Ward J. H. Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 1963, vol. 58, pp. 236-244.</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>
