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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">voprstat</journal-id><journal-title-group><journal-title xml:lang="ru">Вопросы статистики</journal-title><trans-title-group xml:lang="en"><trans-title>Voprosy Statistiki</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2313-6383</issn><issn pub-type="epub">2658-5499</issn><publisher><publisher-name></publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.34023/2313-6383-2022-29-5-35-45</article-id><article-id custom-type="elpub" pub-id-type="custom">voprstat-1483</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>МАТЕМАТИКО-СТАТИСТИЧЕСКИЕ МЕТОДЫ В АНАЛИЗЕ И ПРОГНОЗИРОВАНИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICAL AND STATISTICAL METHODS IN ANALYSIS AND FORECASTING</subject></subj-group></article-categories><title-group><article-title>Об измерении коинтеграционных соотношений между показателями временных рядов текущего счета платежного баланса и ВВП (на примере Азербайджанской Республики)</article-title><trans-title-group xml:lang="en"><trans-title>On the Measurement of Cointegration Relations Between the Indicators of the Time Series of the Current Account of the Balance of Payments and GDP (On the Example of the Republic of Azerbaijan)</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3225-389X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Айюбова</surname><given-names>Н. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Ayyubova</surname><given-names>N. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Натаван Солтан Айюбова – канд. экон. наук, доцент кафедры математической экономики</p><p>AZ 1148, г. Баку, ул. акад. З. Халилова, д. 33</p></bio><bio xml:lang="en"><p>Natavan S. Ayyubova – Cand. Sci. (Econ.), Associate Professor, Department of Mathematical Economics</p><p>33, Academic Zahid Khalilov Str., Baku, AZ 1148 </p></bio><email xlink:type="simple">nayyubova50@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Бакинский государственный университет</institution><country>Азербайджан</country></aff><aff xml:lang="en"><institution>Baku State University</institution><country>Azerbaijan</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>03</day><month>11</month><year>2022</year></pub-date><volume>29</volume><issue>5</issue><fpage>35</fpage><lpage>45</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Айюбова Н.С., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Айюбова Н.С.</copyright-holder><copyright-holder xml:lang="en">Ayyubova N.S.</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://voprstat.elpub.ru/jour/article/view/1483">https://voprstat.elpub.ru/jour/article/view/1483</self-uri><abstract><p>В статье решается задача построения эконометрической модели (на основе временных рядов макроэкономических показателей), отражающей взаимосвязь между изменениями текущего счета платежного баланса и динамикой ВВП (на примере Азербайджанской Республики).С целью оценки корректности применения математико-статистических методов для анализа влияния внешнеэкономической деятельности страны на конечные результаты ее экономической деятельности произведено тестирование построенной модели. Так, для проверки гипотез о нормальном распределении рядов был использован тест Харке – Бера, о стационарности – расширенный тест Дики – Фуллера (ADF) и тест Квятковского – Филлипса – Шмидта – Шина (KPSS), а также построены гистограммы и коррелограммы.В процессе изучения временных рядов рассматриваемых показателей была выявлена их нестационарность как по результатам дескриптивной статистики, теста Харке – Бера, гистограмм, графиков выборочной автокорреляционной функции (АКФ) и частной автокорреляционной функции (ЧАКФ), так и по тесту Дики – Фуллера. Был применен переход к абсолютным приростам первых и вторых разностей.Кроме того, выполнен тест Йохансена на выявление коинтеграционных соотношений. По его итогам при сравнении линейного и квадратичного трендов с аналогичными характеристиками был выбран линейный, указывающий на наличие коинтеграционного соотношения. После проведения тестов Trace и Maximum Eigenvalue принята альтернативная гипотеза о наличии одного вектора коинтеграции.Полученные результаты позволяют сделать вывод о том, что взаимосвязь между показателями счета текущих операций платежного баланса и ВВП Азербайджана имеет долговременный характер. Они также могут служить основой для построения модели коррекции ошибок.</p></abstract><trans-abstract xml:lang="en"><p>The article solves the problem of constructing an econometric model (based on time series of macroeconomic indicators) that reflects the relationship between changes in the current account of the balance of payments and GDP dynamics (on the example of the Republic of Azerbaijan).In order to assess the correctness of the application of mathematical and statistical methods for analyzing the impact of foreign economic activity on the final results of the country's economic activity, the constructed model was tested. So, to test the hypotheses about the normal distribution of the series, the Jarque–Bera test, the augmented Dickey–Fuller test (ADF), the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test were used, and histograms and correlograms were constructed.In the process of studying the time series of the indicators under consideration, their non-stationarity was revealed both according to the results of descriptive statistics, the Jarque–Bera test, histograms, plots of the sample autocorrelation function (ACF) and partial autocorrelation function (PACF), and according to the Dickey–Fuller test. The transition to absolute increments, that is, to the first differences, was applied. In addition, the Johansen test was performed to identify cointegration relationships. Based on its results, when comparing linear and quadratic trends with similar characteristics, a linear one was chosen, indicating the presence of a cointegration relationship. After carrying out the Trace and Maximum Eigenvalue tests, an alternative hypothesis about the presence of one cointegration vector was accepted.The results obtained allow us to conclude that the relationship between the indicators of the current account of the balance of payments and Azerbaijan's GDP is of a long-term nature. They can also serve as a basis for building an error correction model.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>временной ряд</kwd><kwd>стационарность</kwd><kwd>тест Харке – Бера</kwd><kwd>тест Дики – Фуллера</kwd><kwd>тест Квятковского – Филлипса – Шмидта – Шина (KPSS)</kwd><kwd>тест Йохансена</kwd><kwd>автокорреляционная функция</kwd><kwd>частная автокорреляционная функция</kwd></kwd-group><kwd-group xml:lang="en"><kwd>time series</kwd><kwd>stationarity</kwd><kwd>Jarque – Bera test</kwd><kwd>Dickey – Fuller test</kwd><kwd>Kwiatkowski – Phillips – Schmidt – Shin (KPSS) test</kwd><kwd>Johansen test</kwd><kwd>autocorrelation function</kwd><kwd>private autocorrelation function</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">Kumhof M., Li S., Yan I. Balance of Payments Crises under Inflation Targeting // Journal of International Economics. 2007. Vol. 72. Iss. 1. P. 242–264. doi: https://doi.org/10.1016/j.jinteco.2006.10.002.</mixed-citation><mixed-citation xml:lang="en">Kumhof M., Li S., Yan I. Balance of Payments Crises under Inflation Targeting. Journal of International Economics. 2007;72(1):242–264. Available from: https://doi.org/10.1016/j.jinteco.2006.10.002.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Moreno-Brid J.C. On Capital Flows and the Balance-of-Payments Constrained Growth Model // Journal of Post Keynesian Economics. 1998. Vol. 21. Iss. 2. P. 283– 298. doi: https://doi.org/10.1080/01603477.1998.11490194.</mixed-citation><mixed-citation xml:lang="en">Moreno-Brid J.C. On Capital Flows and the Balance-of-Payments Constrained Growth Model. Journal of Post Keynesian Economics. 1998;21(2):283–298. Available from: https://doi.org/10.1080/01603477.1998.11490194.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Петрикова Е.М. Тенденции развития платежного баланса и международной инвестиционной позиции России // Вопросы статистики. 2019. Т. 26. № 10. С. 46–56. doi: https://doi.org/10.34023/2313-6383-2019-26-10-46-56.</mixed-citation><mixed-citation xml:lang="en">Petrikova E.M. Trends in the Development of the Balance of Payments and the International Investment Position of Russia. Voprosy Statistiki. 2019;26(10):46–56. (In Russ.) Available from: https://doi.org/10.34023/2313-6383-2019-26-10-46-56.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Гурвич Е.Т., Прилепский И.В. Как обеспечить внешнюю устойчивость российской экономики // Вопросы экономики. 2013. № 9. С. 4–39. doi: https://doi.org/10.32609/0042-8736-2013-9-4-39.</mixed-citation><mixed-citation xml:lang="en">Gurvich E., Prilepskiy I. How to Secure External Sustainability of the Russian Economy. Voprosy Ekonomiki. 2013;(9):4–39. (In Russ.) Available from: https://doi.org/10.32609/0042-8736-2013-9-4-39.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Бурдыко Н.М. Анализ и прогнозирование основных показателей платежного баланса Республики Беларусь на основе моделей коррекции ошибок // Математическое моделирование макроэкономических процессов: сб. науч. тр. Минск: НИЭИ Минэкономики РБ, 2005. С. 55–73.</mixed-citation><mixed-citation xml:lang="en">Burdyko N.M. Analysis and Forecasting of the Main Indicators of the Balance of Payments of the Republic of Belarus based on Error Correction Models. In: Collection of Sci. Papers «Mathematical Modeling of Macroeconomic Processes». Minsk: Scientific Institute of Economic Research of the Ministry of Economics of the Republic of Belarus; 2005. Pp. 55–73. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Оруджев Э.Г., Гусейнова С.М. Об одной задаче коинтеграции торговых связей Азербайджана, России, Беларуси и Казахстана // Статистика и Экономика. 2020. Т. 17. № 2. С. 29–39. doi: https://statecon.rea.ru/jour/article/view/1463.</mixed-citation><mixed-citation xml:lang="en">Orudzhev E.G., Huseynova S.M. On One Co-Integration Issue of Trade Links of Azerbaijan, Russia, Belarus and Kazakhstan. Statistics and Economics. 2020;17(2):29–39. (In Russ.) Available from: https://doi.org/10.21686/2500-3925-2020-2-29-39.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Orudzhev E.G., Ayyubova N.S. Empirical Analysis of Balance of Payments Dynamics // Caspian Journal of Applied Mathematics, Ecology and Economics. 2020. Vol. 8. No 1. P. 3–9. URL: http://cjamee.org/wp-content/uploads/2021/02/v8i1_1.pdf.</mixed-citation><mixed-citation xml:lang="en">Orudzhev E.G., Ayyubova N.S. Empirical Analysis of Balance of Payments Dynamics. Caspian Journal of Applied Mathematics, Ecology and Economics. 2020;8(1):3–9. (In Russ) Available from: http://cjamee.org/wp-content/uploads/2021/02/v8i1_1.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Айюбова Н.С. Эконометрический анализ и моделирование динамики развития платежного баланса в Азербайджане // Статистика и Экономика. 2022. Т. 19. № 2. С. 14–22. doi: https://doi.org/10.21686/2500-3925-2022-2-14-22.</mixed-citation><mixed-citation xml:lang="en">Ayyubova N.S. Econometric Analysis and Modeling of the Dynamics of the Balance of Payments’ Development in Azerbaijan. Statistics and Economics. 2022;19(2):14–22. (In Russ) Available from: https://doi.org/10.21686/2500-3925-2022-2-14-22.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Oруджев Э.Г., Айюбова Н.С. Эмпирический анализ факторов влияния на платежный баланс Азербайджана // Актуальні проблеми економіки / Actual Problems in Economics. 2016. № 7(181). С. 400–411. URL: https://www.researchgate.net/publication/345308676_empiriceskij_analiz_faktorov_vliania_na_plateznyj_balans_v_azerbajdzane.</mixed-citation><mixed-citation xml:lang="en">Orudzhev E.G., Ayyubova N.S. Empirical Analysis of the Factors Influencing the Balance of Payments in Azerbaijan. Actual Problems of Economics. Scientific Economic Journal. 2016;7(181):400–411. (In Russ) Available from: https://www.researchgate.net/publication/345308676_empiriceskij_analiz_faktorov_vliania_na_plateznyj_balans_v_azerbajdzane.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Franses P-H., Kunst R.M. On the Role of Seasonal Intercepts in Seasonal Cointegration // Oxford Bulletin of Economics and Statistics. 1999. Vol. 61. Iss. 3. P. 409–433. doi: https://doi.org/10.1111/1468-0084.00136.</mixed-citation><mixed-citation xml:lang="en">Franses P-H., Kunst R.M. On the Role of Seasonal Intercepts in Seasonal Cointegration. Oxford Bulletin of Economics and Statistics. 1999;61(3):409–433. Available from: https://doi.org/10.1111/1468-0084.00136.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Dickey D.A., Fuller W.A. Distribution of Estimators for Autoregressive Time Series with a Unit Root // Journal of the American Statistical Association. 1979. Vol. 74. No. 366. P. 427–431. doi: https://doi.org/10.2307/2286348.</mixed-citation><mixed-citation xml:lang="en">Dickey D.A., Fuller W.A. Distribution of Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 1979;74(366):427– 431. Available from: https://doi.org/10.2307/2286348.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Hamilton J.D. Time Series Analyses. Princeton, New Jersey: Princeton University Press, 2001.</mixed-citation><mixed-citation xml:lang="en">Hamilton P. Time Series Analyses. Princeton University Press; 2001.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Engle R.F., Yoo B.S. Cointegrated Economic Time Series: An Overview with New Results // R.F. Engle, C.W.J. Granger (eds). Long-Run Economic Relationships: Readings in Cointegration. London: Oxford University Press, 1991. P. 237–266.</mixed-citation><mixed-citation xml:lang="en">Engle R.F., Yoo B.S. Cointegrated Economic Time Series: An Overview with New Results. In: Engle R.F., Granger C.W.J. (eds) Long-Run Economic Relationships: Readings in Cointegration. Oxford: Oxford University Press; 1991. Pp. 237–266. Available from: https://doi.org/10.1016/0304-4076(93)90016-X.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Канторович Г.Г. Анализ временных рядов. // Экономический журнал ВШЭ. 2003. Т. 7. № 1. С. 79–103.</mixed-citation><mixed-citation xml:lang="en">Kantorovich G.G. Time Series Analysis. The HSE Economic Journal. 2003;7(1):79–103. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Матюшок В.М., Балашова С.А., Лазанюк И.В. Основы эконометрического моделирования c использованием Eviews: учеб. пос. 2-е изд., перераб. и доп. М.: РУДН, 2011. 206 с.</mixed-citation><mixed-citation xml:lang="en">Matyushok V.M., Balashova S.A., Lazanyuk I.V. Fundamentals of Econometric Modeling Using EViews. Tutorial. 2nd ed., updated and revised. Moscow: RUDN; 2011. 206 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Банников В.А. Векторные модели авторегрессии и коррекции регрессионных остатков (Eviews) // Прикладная эконометрика. 2006. № 3. С. 96–129.</mixed-citation><mixed-citation xml:lang="en">Bannikov V.A. Vector Models of Autoregression and Correction of Regression Residuals (Eviews). Applied Econometrics. 2006;(3):96–129. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Johansen S., Juselius K. Identification of the LongRun and the Short-Run Structure: An Application to the ISLM Model // Journal of Econometrics. 1994. Vol. 63. Iss. 1. P. 7–36. doi: https://doi.org/10.1016/0304-4076(93)01559-5.</mixed-citation><mixed-citation xml:lang="en">Johansen S., Juselius K. Identification of the Long-Run and the Short-Run Structure: An Application to the ISLM Model. Journal of Econometrics. 1994;63(1):7– 36. Available from: https://doi.org/10.1016/0304-4076(93)01559.</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>
