{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:37:21Z","timestamp":1787225841522,"version":"build-2736575974"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"vor","delay-in-days":1950,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF-DMS-1505367"],"award-info":[{"award-number":["NSF-DMS-1505367"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF-CMMI-1536978"],"award-info":[{"award-number":["NSF-CMMI-1536978"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,3,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper presents a novel non-linear framework for the construction of flexible multivariate dependence structure (i.e. copulas) from existing copulas based on a straightforward \u2018pairwise max-\u2019rule. The newly constructed max-copula has a closed form and has strong interpretability. Compared with the classical \u2018linear symmetric\u2019 mixture copula, the max-copula can be viewed as a \u2018non-linear asymmetric\u2019 framework. It is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non-extremal behaviour modelling. Max-copulas that are based on single-factor and block factor models are developed to offer parsimonious modelling for structured dependence, especially in high dimensional applications. Combined with semiparametric time series models, the max-copula can be used to develop flexible and accurate models for multivariate time series. A new semiparametric composite maximum likelihood method is proposed for parameter estimation, where the consistency and asymptotic normality of estimators are established. The flexibility of the max-copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments. Real data applications in value-at-risk estimation and portfolio optimization for financial risk management demonstrate the max-copula's promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market.<\/jats:p>","DOI":"10.1111\/rssb.12256","type":"journal-article","created":{"date-parts":[[2017,10,19]],"date-time":"2017-10-19T10:28:37Z","timestamp":1508408917000},"page":"409-432","source":"Crossref","is-referenced-by-count":15,"title":["Semiparametric Dynamic Max-Copula Model for Multivariate Time Series"],"prefix":"10.1093","volume":"80","author":[{"given":"Zifeng","family":"Zhao","sequence":"first","affiliation":[{"name":"University of Wisconsin\u2014Madison , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengjun","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of Wisconsin\u2014Madison , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,10,19]]},"reference":[{"key":"2023022101103934400_","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.insmatheco.2007.02.001","article-title":"Pair-copula constructions of multiple dependence","volume":"44","author":"Aas","year":"2009","journal-title":"Insur. 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