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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.4 20241031//EN" "https://jats.nlm.nih.gov/archiving/1.4/JATS-archive-oasis-article1-4-mathml3.dtd">
<article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" 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" article-type="research-article" xml:lang="ru"><front><journal-meta><issn publication-format="print">2411-1406</issn><issn publication-format="electronic">2411-1406</issn></journal-meta><article-meta><article-id pub-id-type="doi">10.17059/ekon.reg.2025-2-7</article-id><title-group xml:lang="en"><article-title>The Impact of Industrial Output and Investment  on Electricity Consumption in Sverdlovsk Oblast (Russia):  Wavelet Analysis of Time Series Accounting for Seasonal Factors</article-title></title-group><title-group xml:lang="ru"><article-title>Влияние объема промышленного производства и инвестиций на электропотребление в Свердловской области: вейвлет-анализ временных рядов с учетом сезонных факторов</article-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3832-3978</contrib-id><name-alternatives><name xml:lang="en"><surname>Serkov</surname><given-names>Leonid A. </given-names></name><name xml:lang="ru"><surname>Серков </surname><given-names>Леонид Александрович</given-names></name></name-alternatives><email>serkov.la@uiec.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3043-6302</contrib-id><name-alternatives><name xml:lang="en"><surname>Petrov </surname><given-names>Mikhail B. </given-names></name><name xml:lang="ru"><surname>Петров </surname><given-names>Михаил Борисович </given-names></name></name-alternatives><email>petrov.mb@uiec.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Institute of Economics of the Ural Branch of RAS</institution></aff><aff><institution xml:lang="ru">Институт экономики УрО РАН</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-03-26" publication-format="electronic"/><volume>21</volume><issue>2</issue><fpage>349</fpage><lpage>363</lpage><history><date date-type="received" iso-8601-date="2025-01-17"/><date date-type="accepted" iso-8601-date="2024-03-08"/></history><permissions><copyright-statement xml:lang="ru">Copyright © 2025  </copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru"> </copyright-holder><ali:free_to_read/><license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/"><ali:license_ref>https://creativecommons.org/licenses/by/4.0/</ali:license_ref></license></permissions><self-uri content-type="html" mimetype="text/html" xlink:title="article webpage" xlink:href="https://www.economyofregions.org/ojs/index.php/er/article/view/1168">https://www.economyofregions.org/ojs/index.php/er/article/view/1168</self-uri><self-uri content-type="pdf" mimetype="application/pdf" xlink:title="article pdf" xlink:href="https://www.economyofregions.org/ojs/index.php/er/article/download/1168/423">https://www.economyofregions.org/ojs/index.php/er/article/download/1168/423</self-uri><abstract xml:lang="en"><p>This article examines the influence of industrial production and investment on electricity consumption in Sverdlovsk Oblast using multivariate wavelet analysis (MWA) that accounts for seasonal factors. The novelty of the study lies in the application of MWA tools, such as multiple and partial coherence, partial phase difference, and partial wavelet gain coefficient, to identify time-varying causal relationships. The wavelet-based results confirm and extend findings gained through the application of traditional econometric approaches by revealing how these relationships differ across time horizons and frequencies. The multiple coherence analysis shows seasonal cointegration at a frequency corresponding to a four-quarter cycle and the absence of long-term (non-seasonal) cointegration. Partial coherence diagrams suggest that, after controlling for one variable, there is no cointegration between electricity consumption and either industrial output or investment across all frequencies. Partial phase difference analysis reveals the lead-lag structure and phase alignment among the variables, depending on the frequency and time period. Notably, data from 2022–2023, coinciding with the imposition of international sanctions on Russia, offer particularly valuable insights. The study shows that both business cycle theories and related government policies should place greater emphasis on seasonal dynamics. Companies can use the results of wavelet analysis to determine the optimal timing for launching new production capacities.</p></abstract><abstract xml:lang="ru"><p>Электроэнергетика играет ключевую роль в развитии производительных сил, пространственном развитии и интеграции регионов. Наибольший объем потребления электроэнергии приходится на реальный сектор экономики. В связи с этим, анализ взаимосвязей между электропотреблением, объемом промышленного производства и инвестициями на этапе перехода к росту производства приобретает высокую актуальность для развития электроэнергетики и всей экономики. В статье представлен анализ влияния объемов промышленного производства и инвестиций на электропотребление в Свердловской области. Для исследования использованы методы многомерного вейвлет-анализа (MWA), такие как множественная и частичная когерентность, частичная разность фаз и коэффициент частичного вейвлет-усиления применительно к временным рядам с циклической составляющей. В отличие от традиционного эконометрического анализа, результаты, полученные с помощью вейвлет-подхода, не только более детально описывают корреляционные взаимосвязи эндогенной переменой с комбинацией экзогенных, но и содержательно обогащают их выявлением причинно-следственных связей, характер которых различается в зависимости от временного интервала и горизонта планирования. В частности, модели показывают парциальную зависимость спроса на электроэнергию от объема инвестиций в основной капитал Свердловской области, выросшего на 25,7 % за 2023 г. по сравнению с 2022 г. При этом выявлена синфазность электропотребления с объемом инвестиций и лидирование переменной объема инвестиций. Полученные в статье результаты свидетельствуют и о том, что моделирование бизнес-циклов, а также государственная политика в отношении циклических процессов должны учитывать взаимосвязи цикличности представляющих изучаемые процессы переменных, и в этих целях могут быть использованы рассмотренные в статье методы и модели.</p></abstract><kwd-group xml:lang="en"><kwd>production volume</kwd><kwd>investment</kwd><kwd>electricity consumption</kwd><kwd>time series seasonality</kwd><kwd>cointegration</kwd><kwd>multivariate wavelet analysis</kwd><kwd>multiple and partial coherence</kwd><kwd>wavelet gain</kwd><kwd>partial phase difference</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>объем производства</kwd><kwd>инвестиции</kwd><kwd>электропотребление</kwd><kwd>сезонность временных рядов</kwd><kwd>коинтеграция</kwd><kwd>многомерный вейвлет-анализ</kwd><kwd>множественная и частичная когерентность</kwd><kwd>вейвлет-усиление</kwd><kwd>частичная разность фаз</kwd></kwd-group></article-meta></front><body/><back><ack xml:lang="en"><p>This article has been prepared in accordance with the 2025 research plan of the Institute of Economics of the Ural Branch of RAS.</p></ack><ack xml:lang="ru"><p>Статья подготовлена в соответствии с Планом НИР Института экономики УрО РАН на 2025 г.</p></ack><ref-list><ref id="ref1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Астафьева, Н. М. (1996). Вейвлет-анализ: основы теории и примеры применения. Успехи физических наук, 166(11), 1145–1170. https://doi.org/10.3367/UFNr.0166.199611a.1145</mixed-citation><mixed-citation xml:lang="en">Aguiar-Conraria, L. A., Martins, M. M., &amp; Soares, M. J. (2018). Estimating the Taylor rule in the time-frequency domain. </mixed-citation></citation-alternatives></ref><ref id="ref2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Бессонов, В. А., Петроневич, А. В. (2013). Сезонная корректировка как источник ложных сигналов. Экономический журнал ВШЭ, 17(4), 586–616.</mixed-citation><mixed-citation xml:lang="en">Aguiar-Conraria, L., Azevedo, N., &amp; Soares, M. J. (2008). Using wavelets to decompose the time–frequency effects of monetary policy. Physica A: Statistical Mechanics and its Applications, 387(12), 2863–2878. https://doi.org/10.1016/j.physa.2008.01.063</mixed-citation></citation-alternatives></ref><ref id="ref3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Витязев, В. В. (2001). Вейвлет-анализ временных рядов. Санкт-Петербург: Изд-во С.-Петерб. ун-та, 58.</mixed-citation><mixed-citation xml:lang="en">Astaf’eva, N. M. (1996). Wavelet analysis: basic theory and some applications. Uspekhi fizicheskikh nauk [Physics-Uspekhi], 166(11), 1145–1170. https://doi.org/10.1070/pu1996v039n11abeh000177 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Мицель, А. А., Шемякина, А. Н. (2013). Анализ затрат предприятия с помощью вейвлет-преобразований. Экономико-математическое моделирование, (46(349)), 52–60.</mixed-citation><mixed-citation xml:lang="en">Avdakovic, S., Ademovic, A., &amp; Nuhanovic, A. (2013). Correlation between air temperature and electricity demand by linear regression and wavelet coherence approach: UK, Slovakia and Bosnia and Herzegovina case study. Archives of Electrical Engineering, 62(4), 521–532. http://dx.doi.org/10.2478/aee-2013–0042</mixed-citation></citation-alternatives></ref><ref id="ref5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Петров, М., Серков, Л. (2024). Анализ долгосрочных и краткосрочных взаимосвязей между электропотреблением и экономическим ростом в промышленно развитых регионах России. Journal of Applied Economic Research, 23(1), 136–158. https://doi.org/10.15826/vestnik.2024.23.1.006</mixed-citation><mixed-citation xml:lang="en">Bai, J., &amp; Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146(2), 304–317. https://doi.org/10.1016/j.jeconom.2008.08.010</mixed-citation></citation-alternatives></ref><ref id="ref6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Серков, Л. А. (2025). Анализ взаимосвязей инфляции, обменного курса и расходов домохозяйств в экономике России с применением вейвлет-анализа. Journal of Applied Economic Research, 24(1), 59–90. https://doi.org/10.15826/vestnik.2025.24.1.003</mixed-citation><mixed-citation xml:lang="en">Bessonov, V., &amp; Petronevich, A. (2013). Seasonal adjustment as a source of spurious signals. Ehkonomicheskii zhurnal VSHEH [HSE Economic Journal], 17(4), 586–616. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Aguiar-Conraria, L. A., Martins, M. M., &amp; Soares, M. J. (2018). Estimating the Taylor rule in the time-frequency domain.</mixed-citation><mixed-citation xml:lang="en">Bruzda, J. (2020). The wavelet scaling approach to forecasting: Verification on a large set of noisy data. Journal of Forecasting, 39(3), 353–367. https://doi.org/10.1002/for.2634</mixed-citation></citation-alternatives></ref><ref id="ref8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Aguiar-Conraria, L., Azevedo, N., &amp; Soares, M. J. (2008). Using wavelets to decompose the time–frequency effects of monetary policy. Physica A: Statistical Mechanics and its Applications, 387(12), 2863–2878. https://doi.org/10.1016/j.physa.2008.01.063</mixed-citation><mixed-citation xml:lang="en">Connor, J., &amp; Rossiter, R. (2005). Wavelet transforms and commodity prices, Studies in Nonlinear Dynamics. Econometrics, 9(1). https://doi.org/10.2202/1558–3708.1170</mixed-citation></citation-alternatives></ref><ref id="ref9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Avdakovic, S., Ademovic, A., &amp; Nuhanovic, A. (2013). Correlation between air temperature and electricity demand by linear regression and wavelet coherence approach: UK, Slovakia and Bosnia and Herzegovina case study. Archives of Electrical Engineering, 62(4), 521–532. http://dx.doi.org/10.2478/aee-2013–0042</mixed-citation><mixed-citation xml:lang="en">Crowley, P. M. (2007). A guide to wavelets for economists. Journal of Economic Surveys, 21(2), 207–267. https://doi.org/10.1111/j.1467–6419.2006.00502.x</mixed-citation></citation-alternatives></ref><ref id="ref10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Bai, J., &amp; Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146(2), 304–317. https://doi.org/10.1016/j.jeconom.2008.08.010</mixed-citation><mixed-citation xml:lang="en">Engle, R. F., Granger, C. W. J., Hylleberg, S., &amp; Lee, H. S. (1993). The Japanese consumption function. Journal of Econometrics, 55(1-2), 275-298. https://doi.org/10.1016/0304–4076(93)90016-X</mixed-citation></citation-alternatives></ref><ref id="ref11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Bruzda, J. (2020). The wavelet scaling approach to forecasting: Verification on a large set of noisy data. Journal of Forecasting, 39(3), 353–367. https://doi.org/10.1002/for.2634</mixed-citation><mixed-citation xml:lang="en">Foufoula-Georgiou, E., &amp; Kumar, P. (1994). Wavelets in Geophysics in Wavelet Analysis and Its Applications. Academic Press.</mixed-citation></citation-alternatives></ref><ref id="ref12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Connor, J., &amp; Rossiter, R. (2005). Wavelet transforms and commodity prices, Studies in Nonlinear Dynamics. Econometrics, 9(1). https://doi.org/10.2202/1558–3708.1170</mixed-citation><mixed-citation xml:lang="en">Grinsted, A., Moore, J. C., &amp; Jevrejeva, S. (2004). Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 11(5/6), 561–566. https://doi.org/10.5194/npg-11-561-2004</mixed-citation></citation-alternatives></ref><ref id="ref13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Crowley, P. M. (2007). A guide to wavelets for economists.  Journal of Economic Surveys, 21 (2), 207–267. https://doi.org/10.1111/j.1467–6419.2006.00502.x</mixed-citation><mixed-citation xml:lang="en">Hylleberg, S., Engle, R. F., Granger, C. W., &amp; Yoo, B. S. (1990). Seasonal Integration and Cointegration. Journal of Econometrics, 44(1-2), 215–238. </mixed-citation></citation-alternatives></ref><ref id="ref14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Engle, R. F., Granger, C. W. J., Hylleberg, S., &amp; Lee, H. S. (1993). The Japanese consumption function. Journal of Econometrics, 55(1-2), 275-298. https://doi.org/10.1016/0304–4076(93)90016-X</mixed-citation><mixed-citation xml:lang="en">Kirikkaleli, D., &amp; Sowah, J. K. (2020). A wavelet coherence analysis: Nexus between urbanization and environmental sustainability. Environmental Science and Pollution Research, 27(24), 30295–30305. https://doi.org/10.1007/s11356-020-09305-y</mixed-citation></citation-alternatives></ref><ref id="ref15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Foufoula-Georgiou, E., &amp; Kumar, P. (1994). Wavelets in Geophysics in Wavelet Analysis and Its Applications. Academic Press.</mixed-citation><mixed-citation xml:lang="en">Kirikkaleli, D., Adedoyin, F. F., &amp; Bekun, F. V. (2021). Nuclear energy consumption and economic growth in the UK: Evidence from wavelet coherence approach. Journal of Public Affairs, 21(1), e2130. https://doi.org/10.1002/pa.2130</mixed-citation></citation-alternatives></ref><ref id="ref16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Grinsted, A., Moore, J. C., &amp; Jevrejeva, S. (2004). Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 11(5/6), 561–566. https://doi.org/10.5194/npg-11-561-2004</mixed-citation><mixed-citation xml:lang="en">Krüger, J. (2021). A Wavelet Evaluation of Some Leading Business Cycle Indicators for the German Economy. Journal of Business Cycle Research, 17, 293–319. https://doi.org/10.1007/s41549-021-00060-8</mixed-citation></citation-alternatives></ref><ref id="ref17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Hylleberg, S., Engle, R. F., Granger, C. W., &amp; Yoo, B. S. (1990). Seasonal Integration and Cointegration. Journal of Econometrics, 44(1-2), 215–238. </mixed-citation><mixed-citation xml:lang="en">Labat, D. (2010). Cross wavelet analyses of annual continental freshwater discharge and selected climate indices. Journal of Hydrology, 385(1-4), 269–278. https://doi.org/10.1016/j.jhydrol.2010.02.029</mixed-citation></citation-alternatives></ref><ref id="ref18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Kirikkaleli, D., &amp; Sowah, J. K. (2020). A wavelet coherence analysis: Nexus between urbanization and environmental sustainability. Environmental Science and Pollution Research, 27(24), 30295–30305. https://doi.org/10.1007/s11356-020-09305-y</mixed-citation><mixed-citation xml:lang="en">Magazzino, C., &amp; Giolli, L. (2021). The relationship among railway networks, energy consumption, and real added value in Italy. Evidence form ARDL and Wavelet analysis. Research in Transportation Economics, 90, 101126. http://dx.doi.org/10.1016/j.retrec.2021.101126 </mixed-citation></citation-alternatives></ref><ref id="ref19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Kirikkaleli, D., Adedoyin, F. F., &amp; Bekun, F. V. (2021). Nuclear energy consumption and economic growth in the UK: Evidence from wavelet coherence approach. Journal of Public Affairs, 21(1), e2130. https://doi.org/10.1002/pa.2130</mixed-citation><mixed-citation xml:lang="en">Mitsel’, A. A., &amp; Shemiakina, A. N. (2013). Analysis of costs of the enterprise using wavelet-transform. Ekonomiko-matematicheskoe modelirovanie [Economic-Mathematical Modeling], (46(349)), 52–60. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Krüger, J. (2021). A Wavelet Evaluation of Some Leading Business Cycle Indicators for the German Economy. Journal of Business Cycle Research, 17, 293–319. https://doi.org/10.1007/s41549-021-00060-8</mixed-citation><mixed-citation xml:lang="en">Petrov, M. B., &amp; Serkov, L. A. (2024). Analysis of Long-Term and Short-Term Relationships between Electricity Consumption and Economic Growth in Industrialized Regions of Russia. Journal of Applied Economic Research, 23(1), 136–158. https://doi.org/10.15826/vestnik.2024.23.1.006 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Labat, D. (2010). Cross wavelet analyses of annual continental freshwater discharge and selected climate indices. Journal of Hydrology, 385(1-4), 269–278. https://doi.org/10.1016/j.jhydrol.2010.02.029</mixed-citation><mixed-citation xml:lang="en">Rua, A. (2012). Wavelets in Economics. Economic Bulletin and Financial Stability Report Articles, 8, 71–79.</mixed-citation></citation-alternatives></ref><ref id="ref22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Magazzino, C., &amp; Giolli, L. (2021). The relationship among railway networks, energy consumption, and real added value in Italy. Evidence form ARDL and Wavelet analysis. Research in Transportation Economics, 90, 101126. http://dx.doi.org/10.1016/j.retrec.2021.101126 </mixed-citation><mixed-citation xml:lang="en">Rua, A. (2013). Worldwide synchronization since the nineteenth century: A wavelet-based view. Applied Economics Letters, 20(8), 773–776. </mixed-citation></citation-alternatives></ref><ref id="ref23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Rua, A. (2012). Wavelets in Economics. Economic Bulletin and Financial Stability Report Articles, 8, 71–79.</mixed-citation><mixed-citation xml:lang="en">Senjyu, T., Tamaki, Y., Takara, H., &amp; Uezato, K. (2002). Next day load curve forecasting using wavelet analysis with neural network. Electric Power Components and Systems, 30(11), 1167–1178. https://doi.org/10.1080/15325000290085398</mixed-citation></citation-alternatives></ref><ref id="ref24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Rua, A. (2013). Worldwide synchronization since the nineteenth century: A wavelet-based view. Applied Economics Letters, 20(8), 773–776. </mixed-citation><mixed-citation xml:lang="en">Serkov, L. A. (2025). Analysis of the Relationship between Inflation, Exchange Rate and Household Expenditures in the Russian Economy Using Wavelet Analysis. Journal of Applied Economic Research, 24(1), 59–90. https://doi.org/10.15826/vestnik.2025.24.1.003 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Senjyu, T., Tamaki, Y., Takara, H., &amp; Uezato, K. (2002). Next day load curve forecasting using wavelet analysis with neural network. Electric Power Components and Systems, 30(11), 1167–1178. https://doi.org/10.1080/15325000290085398</mixed-citation><mixed-citation xml:lang="en">Torrence, C., &amp; Compo, G. P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79(1), 61–78. https://doi.org/10.1175/1520–0477(1998)079 %3C0061:APGTWA%3E2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="ref26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Torrence, C., &amp; Compo, G. P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79(1), 61–78. https://doi.org/10.1175/1520–0477(1998)079 %3C0061:APGTWA%3E2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Vityazev V. V. (2001). Wejwlet-analis wremennych rjadow [Wavelet analysis of time series], SPb: SPbGU, 58 P. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="ref27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Wu, J., Abban, O. J., Boadi, A. D., Addae, E. A., Akhtar, M., Hongxing, Y., &amp; Ofori, C. (2022). Time–frequency contained co-movement of renewable electricity production, globalization, and СО2 emissions: A wavelet-based analysis in Asia. Energy Reports, 8, 15189–15205. https://doi.org/10.1016/j.egyr.2022.11.054</mixed-citation><mixed-citation xml:lang="en">Wu, J., Abban, O. J., Boadi, A. D., Addae, E. A., Akhtar, M., Hongxing, Y., &amp; Ofori, C. (2022). Time–frequency contained co-movement of renewable electricity production, globalization, and СО2 emissions: A wavelet-based analysis in Asia. Energy Reports, 8, 15189–15205. https://doi.org/10.1016/j.egyr.2022.11.054</mixed-citation></citation-alternatives></ref><ref id="ref28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, Q., &amp; Liu, T. (2010). Research on mid-long term load forecasting base on wavelet neural network. In 2010 Second International Conference on Computer Engineering and Applications (Vol. 2, pp. 217-220). IEEE. https://doi.org/10.1109/ICCEA.2010.195</mixed-citation><mixed-citation xml:lang="en">Zhang, Q., &amp; Liu, T. (2010). Research on mid-long term load forecasting base on wavelet neural network. In 2010 Second International Conference on Computer Engineering and Applications (Vol. 2, pp. 217-220). IEEE. https://doi.org/10.1109/ICCEA.2010.195</mixed-citation></citation-alternatives></ref></ref-list></back></article>