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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Economics and Mathematical Methods</journal-id><journal-title-group><journal-title xml:lang="en">Economics and Mathematical Methods</journal-title><trans-title-group xml:lang="ru"><trans-title>Экономика и математические методы</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0424-7388</issn><issn publication-format="electronic">3034-6177</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">684544</article-id><article-id pub-id-type="doi">10.31857/S0424738825020108</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Mathematical analysis of economic models</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Математический анализ экономических моделей</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Wavelet analysis of the relationship between energy prices and stock indices of high ESG-rating companies: Investment diversification opportunities</article-title><trans-title-group xml:lang="ru"><trans-title>Вейвлет-анализ взаимосвязи между ценами на энергоресурсы и индексами акций компаний с высокими ESG-рейтингами: возможности диверсификации инвестиций</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Sokolova</surname><given-names>Т. V.</given-names></name><name xml:lang="ru"><surname>Соколова</surname><given-names>Т. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>tv.sokolova@hse.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Gurov</surname><given-names>S. V.</given-names></name><name xml:lang="ru"><surname>Гуров</surname><given-names>С. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>sgurov@hse.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Medvedev</surname><given-names>V. А.</given-names></name><name xml:lang="ru"><surname>Медведев</surname><given-names>В. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>medvedev.v@hse.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Lysenko</surname><given-names>V. V.</given-names></name><name xml:lang="ru"><surname>Лысенко</surname><given-names>В. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>vlysenko@hse.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">National Research University “Higher School of Economics”</institution></aff><aff><institution xml:lang="ru">НИУ «Высшая школа экономики»</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-07-04" publication-format="electronic"><day>04</day><month>07</month><year>2025</year></pub-date><volume>61</volume><issue>2</issue><issue-title xml:lang="ru"/><fpage>128</fpage><lpage>142</lpage><history><date date-type="received" iso-8601-date="2025-06-16"><day>16</day><month>06</month><year>2025</year></date><date date-type="accepted" iso-8601-date="2025-06-16"><day>16</day><month>06</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Российская академия наук</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0424-7388/article/view/684544">https://journals.eco-vector.com/0424-7388/article/view/684544</self-uri><abstract xml:lang="en"><p>Our research is the first attempt to identify relationships between «Brent» oil and natural gas prices and indices of stocks of companies with high ESG-ratings (ESG-leaders) in the time and frequency domains. We use such methods in the wavelet analysis framework as analysis of quadratic wavelet coherence and phase difference between data series. Our study is based on daily data from 2018 to the beginning of 2024, which allows us to cover periods of relative macroeconomic stability (until 2020), the COVID-19 coronavirus pandemic (2020–2021) and growing geopolitical tensions in the world (from 2022). We consider ESG-indices of the global market, US and EU markets. Our study shows areas of low and high consistency between energy prices and ESG-leaders’ indices for the three periods under examination and identifies lag and lead relationships between the two considered asset classes. Identifying areas of low consistency allows an investor to develop investment diversification strategies, including hedging against drops in oil and gas prices during global crises. We find that global and US ESG-leaders’ indices provide opportunities for diversifying investments in natural gas futures.</p></abstract><trans-abstract xml:lang="ru"><p>Мы впервые выявляем взаимосвязи между ценами на нефть «Brent» и природный газ и индексами акций компаний с высокими ESG-рейтингами во временной и частотной областях. Мы применяем такие методы вейвлет-анализа, как анализ квадратичной вейвлет-когерентности и разности фаз между рядами данных. Исследование строится на ежедневных данных с 2018 по начало 2024 г., что позволяет охватить периоды относительной макроэкономической стабильности (до 2020 г.), пандемии коронавируса COVID-19 (2020–2021 г.) и роста геополитической напряженности в мире (с 2022 г.). Мы рассматриваем ESG-индексы глобального рынка, рынков США и ЕС. В нашем исследовании показаны области низкой и высокой согласованности цен на энергоресурсы и ESG-ориентированных индексов для трех рассматриваемых периодов, выявлены соотношения запаздывания и опережения между рассматриваемыми классами активов. Выявление областей низкой согласованности позволяет разработать стратегии диверсификации инвестиций, в том числе для хеджирования от падений цен на нефть и газ в условиях глобальных кризисов. Мы пришли к выводу, что индексы акций компаний–лидеров ESG глобального рынка и рынка США предоставляют возможности для диверсификации инвестиций во фьючерсы на природный газ.</p></trans-abstract><kwd-group xml:lang="en"><kwd>energy resources</kwd><kwd>stock</kwd><kwd>ESG</kwd><kwd>risk diversification</kwd><kwd>wavelet analysis</kwd><kwd>wavelet coherence</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>энергоресурсы</kwd><kwd>акции компаний с высокими ESG-рейтингами</kwd><kwd>диверсификация инвестиций</kwd><kwd>вейвлет-анализ</kwd><kwd>вейвлет-когерентность</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Российский научный фонд</institution></institution-wrap><institution-wrap><institution xml:lang="en">Russian Science Foundation</institution></institution-wrap></funding-source><award-id>23-28-00740</award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Aguiar-Conraria L., Azevedo N., Soares M. 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