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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">msuecon</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Московского университета. Серия 6. Экономика</journal-title><trans-title-group xml:lang="en"><trans-title>Lomonosov Economics Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0130-0105</issn><publisher><publisher-name>MSUPRESS</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">msuecon-268</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>ФИНАНСОВАЯ ЭКОНОМИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FINANCIAL STUDIES</subject></subj-group></article-categories><title-group><article-title>Принцип скользящей верификации как основа для идентификации базовых критериев портфельного анализа</article-title><trans-title-group xml:lang="en"><trans-title>The principle of sliding veriﬁcation as a basis for identiﬁcation of the essential criteria of the portfolio analysis</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2544-8656</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Герцекович</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Gertsekovich</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Герцекович Давид Арташевич — кандидат экономических наук, доцент</p><p>Иркутск</p></bio><bio xml:lang="en"><p>Irkutsk</p></bio><email xlink:type="simple">davidgerc@yahoo.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7017-7272</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бунеева</surname><given-names>Е. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Buneeva</surname><given-names>E. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Бунеева Евгения Юрьевна — кандидат экономических наук, доцент</p><p>Иркутск</p></bio><bio xml:lang="en"><p>Irkutsk</p></bio><email xlink:type="simple">eugorbachevskaya@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6288-0248</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Константинова</surname><given-names>Т. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Konstantinova</surname><given-names>T. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Константинова Татьяна Дмитриевна — студент</p><p>Иркутск</p></bio><bio xml:lang="en"><p>Irkutsk</p></bio><email xlink:type="simple">tanya.konstantinova.2014@mail.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/0000-0002-5933-6081</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Паленая</surname><given-names>Я. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Palennaia</surname><given-names>Ia. K.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Паленная Яна Константиновна — студент</p><p>Иркутск</p><p> </p></bio><bio xml:lang="en"><p>Irkutsk</p></bio><email xlink:type="simple">sagelie@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Иркутский государственный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk State University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Иркутский национальный исследовательский технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk National Research Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>10</day><month>03</month><year>2022</year></pub-date><volume>0</volume><issue>2</issue><fpage>94</fpage><lpage>109</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Герцекович Д.А., Бунеева Е.Ю., Константинова Т.Д., Паленая Я.К., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Герцекович Д.А., Бунеева Е.Ю., Константинова Т.Д., Паленая Я.К.</copyright-holder><copyright-holder xml:lang="en">Gertsekovich D.A., Buneeva E.Y., Konstantinova T.D., Palennaia I.K.</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://msuecon.elpub.ru/jour/article/view/268">https://msuecon.elpub.ru/jour/article/view/268</self-uri><abstract><p>Статья посвящена инвестиционному анализу, одним из наиболее актуальных и востребованных методов которого являются портфельные методы. В традиционной постановке теории портфеля подразумевается, что базовые критерии портфельной теории, такие как ожидаемая доходность и уровень риска, для всех рассматриваемых финансовых инструментов рассчитываются по историческим данным одинаковой длины и остаются неизменными на протяжении всего времени эксплуатации модели. Предлагаемый авторами подход представляет собой модификацию модели Г. Марковица, суть которой заключается в том, что для вычисления ожидаемой доходности и уровня риска для каждого анализируемого финансового инструмента отыскивается своя оптимальная (уникальная) длина обучающей выборки. Поиск экстремума целевой функции осуществляется методом полного перебора (цикловая оптимизация), что обеспечивает достижение глобального экстремума критерия оптимизации при ограничении на предельно допустимый уровень риска. Величина выборки подбирается по двум критериям качества, в основу которых положена точность вырабатываемых прогнозов, а именно: 1) из условия минимума суммы квадратов отклонений прогнозных значений ожидаемой доходности, от ее реальных значений; 2) из условия максимизации таких результатов прогнозов, когда ожидания инвестора оправдались и при минимуме результатов, когда реальная доходность оказалась меньше предполагаемой. Селекция оптимальной длины обучающей выборки осуществляется по принципу скользящей верификации на независимом материале. Изложенная процедура апробирована на реальных примерах: прогноза доходности фондового рынка США и прогнозе прироста урожайности основных сельскохозяйственных культур Российской Федерации. Изложенный алгоритм, положенный в основу синтеза широко диверсифицированных портфелей, позволяет значительно повысить эффективность принимаемых инвестиционных решений, чему способствует учет особенностей как изучаемых рынков, так и соответствующих финансовых инструментов.</p></abstract><trans-abstract xml:lang="en"><p>This article provides the investment analysis, with the portfolio method being one of the frontmost instruments. The traditional portfolio theory implies that its essential criteria such as expected return and risk rate for all considered financial instruments are estimated from the historical data of equal length and are invariant throughout the usage period of the model. The authors suggest the approach which is a development of the Markowitz model. The point being, to estimate the expected return and the risk rate for each financial instrument in focus, an effective (own) learning sample is determined. The extremum seeking for the target function is performed through the method of full enumeration (cycle optimization) which provides the global extremum of the optimization criterion with restriction to the maximum permissible risk level. The sample size is tried upon two quality criteria considering accuracy of forecasts, namely: 1) the minimum condition of the sum of squared deviations of the projected values for the expected return, real values, 2) the maximization of the predicted forecasts when the investor expectations are met, with the minimal results when the real return appeared lower than the predicted one. The selection of the learning sample optimal length is performed on the principle of sliding verification of independent material. The described procedure is tested on realistic examples: the US stock market return forecast and staple crop yield gain forecast in the Russian Federation. The suggested algorithm underlying the synthesis of extensively diversified portfolios improves e investment problem solving effectiveness with contribution of considerations of both the markets in focus and the suitable financial instruments.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>доходность</kwd><kwd>риск</kwd><kwd>теория портфеля</kwd><kwd>идентификация</kwd><kwd>скользящая верификация</kwd><kwd>модель Марковица</kwd><kwd>инвестиционные стратегии</kwd><kwd>принятие решений</kwd></kwd-group><kwd-group xml:lang="en"><kwd>return</kwd><kwd>risk</kwd><kwd>portfolio theory</kwd><kwd>identiﬁcation</kwd><kwd>sliding veriﬁcation</kwd><kwd>Markowitz model</kwd><kwd>investment strategies</kwd><kwd>decision-making</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">Брейли, Р., Майерс, С. (2008). Принципы корпоративных финансов М.:ЗАО «Олимп — Бизнес».</mixed-citation><mixed-citation xml:lang="en">Breyli, R., Mayers, С. (2008). The principles of corporate finance. M.:Company «Olimp — Buisness».</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Герцекович, Д.А., Бабушкин Р.В. (2019). Динамический портфельный анализ мировых фондовых индексов. Мир экономики и управления, Т. 19, № 4. С. 14 – 30. DOI 10.25205/2542-0429-2019-19-4-14-.</mixed-citation><mixed-citation xml:lang="en">Gercekovich, D.А., Babushkin R.V. (2019). Dynamic Portfolio Analysis of World Stock Indexes. World of Economics and Management, V. 19, № 4. С. 14 – 30. DOI 10.25205/2542-0429-2019-19-4-14-.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Герцекович, Д.А. (2008). Количественные методы анализа финансовых рынков Иркутск: Изд-во Иркут. гос. ун-та.</mixed-citation><mixed-citation xml:lang="en">Gercekovich, D.А. (2008). Quantative methods of market analysis. Irkutsk: Irkutsk state university publisher.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Гершенгорн, Г.И. (1977). Пакет программ для построения эмпирических дифференциальных уравнений. Долгосрочные прогнозы природных явлений. Новосибирск : Наука.</mixed-citation><mixed-citation xml:lang="en">Gershengorn, G.I. (1977). A software package for constructing empirical differential equations. Longterm forecasts of natural phenomena. Novosibirsk: Science.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Гитман, Л.Дж., Джонк, М.Д. (1997). Основы инвестирования. М.: Дело.</mixed-citation><mixed-citation xml:lang="en">Gitman, L.Dj., Djonk, M.D. (1997). The basis of investment. М.: Delo.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Грэм, Б. (2018). Разумный инвестор: Полное руководство по стоимостному инвестированию. М.: Альпина Паблишер.</mixed-citation><mixed-citation xml:lang="en">Gram, B. (2018). Reasonable investor: The complete guide to value investing. М.: Alpina Publisher.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Дамодоран, А. (2007). Инвестиционная оценка: Инструменты и методы оценки любых активов. М. : Альпина.</mixed-citation><mixed-citation xml:lang="en">Damodaran, A. (2007). Investment estimation: Tools and methods of estimation of any assets. М. : Alpina.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Инвестиции в России. 2017. Стат. сб. Росстат. М.</mixed-citation><mixed-citation xml:lang="en">Investments in Russia. 2017. Statitics. Rosstat. М.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Кейнс, Дж.М. (2007). Общая теория занятости, процента и денег. Избранное. М.: Эксмо.</mixed-citation><mixed-citation xml:lang="en">Keins, Dj. M. (2007). General theory of employment, interest and money. Favorites. М.: Eksmo.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">ЛеБо, Ч., Лукас, Д.В. (1999). Компьютерный анализ фьючерсных рынков. М. : Альпина.</mixed-citation><mixed-citation xml:lang="en">LeBo, Ch., Lukas, D.V. (1999). Computer analysis of futures markets . М. : Alpina.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Фабоцци, Ф.Дж. (2000). Управление инвестициями. М.: ИНФРА-М.</mixed-citation><mixed-citation xml:lang="en">Fabocci, F.J. (2000). Investments management. М.: INFRA-М.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Ферри, Р. (2013). Все о распределении активов. Легкий способ начать свой путь. М.: Издательство «Манн, Иванов и Фербер».</mixed-citation><mixed-citation xml:lang="en">Ferri, R. (2013). All about asset allocation. An easy way to start your journey. М.: «Mann, Ivaniv, Ferber» Publisher.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Шарп, У., Александер, Г., Бэйли, Дж. (2016). Инвестиции. М.: ИНФРА-М.</mixed-citation><mixed-citation xml:lang="en">Sharp, U., Alexander, G., Beyli, J (2016). Investments. М.: INFRA-М.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Элдер, А. (2003). Как играть и выигрывать на бирже. М. : Диаграмма.</mixed-citation><mixed-citation xml:lang="en">Elder, А. (2003). How to play and win on markets. М. : Diagramma.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Bernstein, U. (2001). The Intelligent Asset Allocator. How to Build Your Portfolio to Maximize Returns and Minimize Risk. The McGraw-Hill Companies, Inc.</mixed-citation><mixed-citation xml:lang="en">Bernstein, U. (2001). The Intelligent Asset Allocator. How to Build Your Portfolio to Maximize Returns and Minimize Risk. The McGraw-Hill Companies, Inc.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">DeBondt, W.F.M., Thaler, R. (1985). Does the stock market overreact? Journal of Finance, Vol. 40, P. 793 – 805.</mixed-citation><mixed-citation xml:lang="en">DeBondt, W.F.M., Thaler, R. (1985). Does the stock market overreact? Journal of Finance, Vol. 40, P. 793 – 805.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">DeBondt, W.F.M., Thaler, R. (1987). Further evidence on investor overreaction and stock market seasonality. Journal of Finance, Vol. 42, P. 557 – 581.</mixed-citation><mixed-citation xml:lang="en">DeBondt, W.F.M., Thaler, R. (1987). Further evidence on investor overreaction and stock market seasonality. Journal of Finance, Vol. 42, P. 557 – 581.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Jegadeesh, N. (1990). Evidence of Predictable Behavior of Security Returns. Journal of Finance, Vol. 45, № 3, P. 890 – 891.</mixed-citation><mixed-citation xml:lang="en">Jegadeesh, N. (1990). Evidence of Predictable Behavior of Security Returns. Journal of Finance, Vol. 45, № 3, P. 890 – 891.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Jegadeesh, N., Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance, Vol. 48, № 1, P. 65 – 91.</mixed-citation><mixed-citation xml:lang="en">Jegadeesh, N., Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance, Vol. 48, № 1, P. 65 – 91.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">O`Shaughnessy, J. (2005). What Works on Wall Street. McGraw-Hill, XVI, p. 273–295.</mixed-citation><mixed-citation xml:lang="en">O`Shaughnessy, J. (2005). What Works on Wall Street. McGraw-Hill, XVI, p. 273–295.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Fisher, I. (1930). The Theory of Interest. The Macmillan Company, N.Y.</mixed-citation><mixed-citation xml:lang="en">Fisher, I. (1930). The Theory of Interest. The Macmillan Company, N.Y.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Gertsekovich, D., Grigorova, L., Peshkov, V. (2019). Return on investment in REIT real estate funds. IOP Conference Series: Materials Science and Engineering, 667 (1), № 012025.</mixed-citation><mixed-citation xml:lang="en">Gertsekovich, D., Grigorova, L., Peshkov, V. (2019). Return on investment in REIT real estate funds. IOP Conference Series: Materials Science and Engineering, 667 (1), № 012025.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Keynes, J.M. (1936). General Theory of Employment, Interest and Money. Harcourt, Brace, N.Y..</mixed-citation><mixed-citation xml:lang="en">Keynes, J.M. (1936). General Theory of Employment, Interest and Money. Harcourt, Brace, N.Y..</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Keynes, J.M. (1937). General Theory of Employment. Economic Journal, Vol. 51, № 2, P. 214.</mixed-citation><mixed-citation xml:lang="en">Keynes, J.M. (1937). General Theory of Employment. Economic Journal, Vol. 51, № 2, P. 214.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47, 1, P. 13 – 37.</mixed-citation><mixed-citation xml:lang="en">Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47, 1, P. 13 – 37.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Markovitz, H.M. (1952). Portfolio selection. J. of Finance, Vol. 7, № 1, P. 77 – 91.</mixed-citation><mixed-citation xml:lang="en">Markovitz, H.M. (1952). Portfolio selection. J. of Finance, Vol. 7, № 1, P. 77 – 91.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Merton, R.C. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3, P. 373 – 413.</mixed-citation><mixed-citation xml:lang="en">Merton, R.C. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3, P. 373 – 413.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Miller, M.H. (1978). Dividends and Taxes, Journal of Financial Economics. M. Scholes, 6.</mixed-citation><mixed-citation xml:lang="en">Miller, M.H. (1978). Dividends and Taxes, Journal of Financial Economics. M. Scholes, 6.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Mossin, J. (1966). Equilibrium in a Capital Asset Markets. Econometrica, Vol. 34, № 4, P. 768 – 783.</mixed-citation><mixed-citation xml:lang="en">Mossin, J. (1966). Equilibrium in a Capital Asset Markets. Econometrica, Vol. 34, № 4, P. 768 – 783.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Roll, R. A. (1977). Critique of the Asset Pricing Theory`s Tests. Part 1. On Past and Potential Testability of the Theory. Journal of Financial Economics, 4, № 2 (March), P. 129 – 176.</mixed-citation><mixed-citation xml:lang="en">Roll, R. A. (1977). Critique of the Asset Pricing Theory`s Tests. Part 1. On Past and Potential Testability of the Theory. Journal of Financial Economics, 4, № 2 (March), P. 129 – 176.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Siegel, J.J. (1992). The Equity Premium: Stock and Bond Returns Since 1802. Financial Analysts Journal, 48, № 1, (January/February), P. 28 – 38.</mixed-citation><mixed-citation xml:lang="en">Siegel, J.J. (1992). The Equity Premium: Stock and Bond Returns Since 1802. Financial Analysts Journal, 48, № 1, (January/February), P. 28 – 38.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Tobin, J., Hahn, F.H., Brechling, F.P.R. (1965). The Theory of Portfolio Selection. Theory of Interest Rates. London: MacMillan.</mixed-citation><mixed-citation xml:lang="en">Tobin, J., Hahn, F.H., Brechling, F.P.R. (1965). The Theory of Portfolio Selection. Theory of Interest Rates. London: MacMillan.</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>
