{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T06:44:34Z","timestamp":1778827474165,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2015,6,26]],"date-time":"2015-06-26T00:00:00Z","timestamp":1435276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71201054"],"award-info":[{"award-number":["71201054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91224001"],"award-info":[{"award-number":["91224001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71433001"],"award-info":[{"award-number":["71433001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["ZZ1315"],"award-info":[{"award-number":["ZZ1315"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a new entropy-optimized bivariate empirical mode decomposition (BEMD)-based model for estimating portfolio value at risk (PVaR). It reveals and analyzes different components of the price fluctuation. These components are decomposed and distinguished by their different behavioral patterns and fluctuation range, by the BEMD model. The entropy theory has been introduced for the identification of the model parameters during the modeling process. The decomposed bivariate data components are calculated with the DCC-GARCH models. Empirical studies suggest that the proposed model outperforms the benchmark multivariate exponential weighted moving average (MEWMA) and DCC-GARCH model, in terms of conventional out-of-sample performance evaluation criteria for the model accuracy.<\/jats:p>","DOI":"10.3390\/e17074519","type":"journal-article","created":{"date-parts":[[2015,6,26]],"date-time":"2015-06-26T10:24:46Z","timestamp":1435314286000},"page":"4519-4532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Estimating Portfolio Value at Risk in the Electricity Markets Using an Entropy Optimized BEMD Approach"],"prefix":"10.3390","volume":"17","author":[{"given":"Yingchao","family":"Zou","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China"},{"name":"College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lean","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaijian","family":"He","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0378-4371(00)00276-4","article-title":"Energy price risk management","volume":"285","author":"Weron","year":"2000","journal-title":"Physica A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1016\/j.energy.2005.02.015","article-title":"Electricity derivatives and risk management","volume":"31","author":"Deng","year":"2006","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dowd, K. 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