{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T03:08:23Z","timestamp":1779246503306,"version":"3.51.4"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2014,12,22]],"date-time":"2014-12-22T00:00:00Z","timestamp":1419206400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p>Understanding the time series dynamics of a multi-dimensional dependency structure is a challenging task. Multivariate covariance driven Gaussian or mixed normal time varying models have only a limited ability to capture important features of the data such as heavy tails, asymmetry, and nonlinear dependencies. The present paper tackles this problem by proposing and analyzing a hidden Markov model (HMM) for hierarchical Archimedean copulae (HAC). The HAC constitute a wide class of models for multi-dimensional dependencies, and HMM is a statistical technique for describing regime switching dynamics. HMM applied to HAC flexibly models multivariate dimensional non-Gaussian time series.<\/jats:p><jats:p>We apply the expectation maximization (EM) algorithm for parameter estimation. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application. This example is motivated by a local adaptive analysis that yields a time varying HAC model. We compare its forecasting performance with that of other classical dynamic models. In another, second, application, we model a rainfall process. This task is of particular theoretical and practical interest because of the specific structure and required untypical treatment of precipitation data.<\/jats:p>","DOI":"10.1017\/s0266466614000607","type":"journal-article","created":{"date-parts":[[2014,12,22]],"date-time":"2014-12-22T11:10:28Z","timestamp":1419246628000},"page":"981-1015","source":"Crossref","is-referenced-by-count":28,"title":["HIDDEN MARKOV STRUCTURES FOR DYNAMIC COPULAE"],"prefix":"10.1017","volume":"31","author":[{"given":"Wolfgang Karl","family":"H\u00e4rdle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ostap","family":"Okhrin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weining","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,12,22]]},"reference":[{"key":"S0266466614000607_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.01.013"},{"key":"S0266466614000607_ref26","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbh006"},{"key":"S0266466614000607_ref6","unstructured":"Caia Z. , Chen X. , Fan Y. , & Wang X. (2006) Selection of Copulas with Applications in Finance. Working paper. Available at http:\/\/www.economics.smu.edu.sg\/femes\/2008\/papers\/219.pdf."},{"key":"S0266466614000607_ref32","doi-asserted-by":"publisher","DOI":"10.1088\/1469-7688\/4\/3\/009"},{"key":"S0266466614000607_ref1","volume-title":"Staff Reports 348","author":"Adrian","year":"2011"},{"key":"S0266466614000607_ref11","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618487"},{"key":"S0266466614000607_ref30","doi-asserted-by":"publisher","DOI":"10.1080\/14697680902821733"},{"key":"S0266466614000607_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jempfin.2006.07.002"},{"key":"S0266466614000607_ref21","doi-asserted-by":"publisher","DOI":"10.1002\/0471721182"},{"key":"S0266466614000607_ref3","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1214\/aos\/1024691255","article-title":"Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models","volume":"26","author":"Bickel","year":"1998","journal-title":"Annals of Statistics"},{"key":"S0266466614000607_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342558"},{"key":"S0266466614000607_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-8162-8_8"},{"key":"S0266466614000607_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.07.027"},{"key":"S0266466614000607_ref7","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-28982-8","volume-title":"Inference in Hidden Markov Models","author":"Capp\u00e9","year":"2005"},{"key":"S0266466614000607_ref17","doi-asserted-by":"publisher","DOI":"10.1524\/strm.2013.2004"},{"key":"S0266466614000607_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.03.004"},{"key":"S0266466614000607_ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the em algorithm (with discussion)","volume":"39","author":"Dempster","year":"1977","journal-title":"Journal of the Royal Statistical Society B"},{"key":"S0266466614000607_ref13","first-page":"165","article-title":"Composite likelihood EM algorithm with applications to multivariate hidden Markov model","volume":"21","author":"Gao","year":"2011","journal-title":"Statistica Sinica"},{"key":"S0266466614000607_ref14","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.0016"},{"key":"S0266466614000607_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/1912559"},{"key":"S0266466614000607_ref16","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbg005"},{"key":"S0266466614000607_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(92)90141-C"},{"key":"S0266466614000607_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS789"},{"key":"S0266466614000607_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS556"},{"key":"S0266466614000607_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.12.001"},{"key":"S0266466614000607_ref25","doi-asserted-by":"publisher","DOI":"10.1017\/S0022109000004294"},{"key":"S0266466614000607_ref28","doi-asserted-by":"publisher","DOI":"10.1109\/5.18626"},{"key":"S0266466614000607_ref31","first-page":"299","article-title":"Fonctions d\u00e9 repartition \u00e1 n dimension et leurs marges","volume":"8","author":"Sklar","year":"1959","journal-title":"Publications de l\u2019Institut de statistique de l\u2019Universit de Paris"},{"key":"S0266466614000607_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9876.2008.00654.x"},{"key":"S0266466614000607_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1056562468"},{"key":"S0266466614000607_ref23","volume-title":"An Introduction to Copulas","author":"Nelsen","year":"2006"},{"key":"S0266466614000607_ref18","doi-asserted-by":"publisher","DOI":"10.1201\/b13150"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466614000607","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T01:14:01Z","timestamp":1717636441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466614000607\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,22]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["S0266466614000607"],"URL":"https:\/\/doi.org\/10.1017\/s0266466614000607","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,22]]}}}