{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:10:07Z","timestamp":1760213407866,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,21]],"date-time":"2016-12-21T00:00:00Z","timestamp":1482278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002649","name":"Yeungnam University","doi-asserted-by":"publisher","award":["215A580013"],"award-info":[{"award-number":["215A580013"]}],"id":[{"id":"10.13039\/501100002649","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2015R1C1A1A01052330"],"award-info":[{"award-number":["NRF-2015R1C1A1A01052330"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we consider a sequential monitoring procedure for detecting changes in copula function. We propose a cusum type of monitoring test based on the empirical copula function and apply it to the detection of the distributional changes in copula function. We investigate the asymptotic properties of the stopping time and show that under regularity conditions, its limiting null distribution is the same as the sup of Kiefer process. Moreover, we utilize the bootstrap method in order to obtain the limiting distribution. A simulation study and a real data analysis are conducted to evaluate our test.<\/jats:p>","DOI":"10.3390\/e18120457","type":"journal-article","created":{"date-parts":[[2016,12,23]],"date-time":"2016-12-23T04:09:09Z","timestamp":1482466149000},"page":"457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Monitoring Test for Stability of Dependence Structure in Multivariate Data Based on Copula"],"prefix":"10.3390","volume":"18","author":[{"given":"Jiyeon","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Statistics, Seoul National University, Seoul 08826, Korea"}]},{"given":"Byungsoo","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Statistics, Yeungnam University, Gyeongsan 38541, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula Methods in Finance, John Wiley & Sons.","DOI":"10.1002\/9781118673331"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cherubini, U., Gobbi, F., Mulinacci, S., and Romagnoli, S. (2012). Dynamic Copula Methods in Finance, John Wiley & Sons.","DOI":"10.1002\/9781118467404"},{"key":"ref_3","unstructured":"McNeil, A.J., Frey, R., and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton Series in Finance."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hougaard, P. (2000). Analysis of Multivariate Survival Data, Springer.","DOI":"10.1007\/978-1-4612-1304-8"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0261-5606(94)00001-H","article-title":"Is the correlation in international equity returns constant: 1960\u20131990?","volume":"14","author":"Longin","year":"1995","journal-title":"J. Int. Money Financ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1111\/j.1468-2354.2006.00387.x","article-title":"Modelling asymmetric exchange rate dependence","volume":"47","author":"Patton","year":"2006","journal-title":"Int. Econ. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.jempfin.2006.07.002","article-title":"Measuring financial contagion: A copula approach","volume":"14","author":"Rodriguez","year":"2007","journal-title":"J. Empir. Financ."},{"key":"ref_8","unstructured":"Szegoe, G. (2004). Risk Measures for the 21st Century, John Wiley & Sons."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1080\/14697680902933041","article-title":"Change analysis of dynamic copula for measuring dependence in multivariate finance data","volume":"10","author":"Guegan","year":"2010","journal-title":"Quant. Financ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.jempfin.2009.10.004","article-title":"Tracking a changing copula","volume":"17","author":"Harvey","year":"2010","journal-title":"J. Empir. Financ."},{"key":"ref_11","first-page":"106","article-title":"When is a copula constant? A test for changing relationships","volume":"9","author":"Busetti","year":"2011","journal-title":"J. Financ. Econom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1111\/j.1467-9892.2011.00763.x","article-title":"Change point detection in copula ARMA-GARCH Models","volume":"33","author":"Na","year":"2012","journal-title":"J. Time Ser. Anal."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1002\/cjs.11150","article-title":"Multivariate Kendall\u2019s tau for change-point detection in copulas","volume":"41","author":"Quessy","year":"2013","journal-title":"Can. J. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.jmva.2012.12.002","article-title":"Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique","volume":"116","author":"Ruppert","year":"2013","journal-title":"J. Multivar. Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.jmva.2014.07.012","article-title":"Detecting changes in cross-sectional dependence in multivariate time series","volume":"132","author":"Kojadinovic","year":"2014","journal-title":"J. Multivar. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.2307\/2171955","article-title":"Monitoring structural change","volume":"64","author":"Chu","year":"1996","journal-title":"Econometrica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.jspi.2003.07.014","article-title":"Monitoring changes in linear models","volume":"126","author":"Kokoszka","year":"2004","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1017\/S0266466604206041","article-title":"Sequential change-point detection in GARCH(p,q) models","volume":"20","author":"Berkes","year":"2004","journal-title":"Econ. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.jmva.2008.08.005","article-title":"Monitoring parameter change in AR(p) time series models","volume":"100","author":"Gombay","year":"2009","journal-title":"J. Multivar. Anal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10260-011-0162-3","article-title":"Monitoring parameter change in time series models","volume":"20","author":"Na","year":"2011","journal-title":"Stat. Methods Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.jkss.2014.08.002","article-title":"Monitoring test for stability of copula parameter in time series","volume":"43","author":"Na","year":"2014","journal-title":"J. Korean Stat. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2969","DOI":"10.1080\/03610920902947261","article-title":"Monitoring distributional changes in autoregressive models","volume":"38","author":"Lee","year":"2009","journal-title":"Commun. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"847","DOI":"10.3150\/bj\/1099579158","article-title":"Weak convergence of empirical copula processes","volume":"10","author":"Fermanian","year":"2004","journal-title":"Bernoulli"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.jmva.2008.05.004","article-title":"Testing for equality between two copulas","volume":"100","author":"Scaillet","year":"2009","journal-title":"J. Multivar. Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1016\/j.spl.2010.08.021","article-title":"A note on bootstrap approximations for the empirical copula process","volume":"80","author":"Dette","year":"2010","journal-title":"Stat. Probab. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"153","DOI":"10.3103\/S1066530712030015","article-title":"On the strong approximation of bootstrapped empirical copula process with applications","volume":"21","author":"Bouzebda","year":"2012","journal-title":"Math. Methods Stat."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Joe, H. (1997). Multivariate Models and Dependence Concepts, Chapman and Hall.","DOI":"10.1201\/9780367803896"},{"key":"ref_28","unstructured":"Nelsen, R.B. (2006). An Introduction to Copulas, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s10182-012-0200-y","article-title":"Change point detection in SCOMDY models","volume":"97","author":"Na","year":"2013","journal-title":"AStA Adv. Stat. Anal."},{"key":"ref_30","first-page":"1","article-title":"An introduction to continuity, extrema, and related topics for general Gaussian processes","volume":"Volume 12","author":"Adler","year":"1990","journal-title":"Institute of Mathematical Statistics Lecture Notes"},{"key":"ref_31","unstructured":"Piterbarg, V.I. (1996). Asymptotic Methods in the Theory of Gaussian Processes and Fields, American Mathematical Society."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0304-4149(88)90068-3","article-title":"A note on strong approximations of multivariate empirical processes","volume":"28","year":"1988","journal-title":"Stoch. Process. Their Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"764","DOI":"10.3150\/11-BEJ387","article-title":"Asymptotics of empirical copula processes under non-restrictive smoothness assumptions","volume":"18","author":"Segers","year":"2012","journal-title":"Bernoulli"},{"key":"ref_34","unstructured":"Tsukahara, H. (2000). Empirical Copulas and Some Applications, Seijo University."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1175\/1520-0442(1993)006<1232:TRBPAT>2.0.CO;2","article-title":"The Relationship between Precipitation and Temperature over the Contiguous United States","volume":"6","author":"Zhao","year":"1992","journal-title":"J. Clim."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1175\/1520-0442(1993)006<1111:MPTRAT>2.0.CO;2","article-title":"Monthly precipitation-temperature relations and temperature prediction over the United States","volume":"6","author":"Huang","year":"1993","journal-title":"J. Clim."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2003WR002456","article-title":"Multivariate hydrological frequency analysis using copulas","volume":"40","author":"Favre","year":"2004","journal-title":"Water Resour. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1002\/hyp.6400","article-title":"Assessment of hydrological droughts for the Yellow River, China, using copulas","volume":"21","author":"Shiau","year":"2007","journal-title":"Hydrol. Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1061\/(ASCE)1084-0699(2007)12:4(381)","article-title":"Using copulas in hydrology: Benefits, cautions, and issues","volume":"12","author":"Dupuis","year":"2007","journal-title":"J. Hydrol. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"761","DOI":"10.5194\/npg-15-761-2008","article-title":"Multivariate non-normally distributed random variables in climate research\u2014Introduction to the copula approach","volume":"15","author":"Friederichs","year":"2008","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s11203-008-9026-3","article-title":"An empirical central limit theorem with applications to copulas under weak dependence","volume":"12","author":"Doukhan","year":"2009","journal-title":"Stat. Inference Stoch. Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jmva.2013.04.003","article-title":"Empirical and sequential empirical copula processes under serial dependence","volume":"119","author":"Volgushev","year":"2013","journal-title":"J. Multivar. Anal."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/12\/457\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:29:00Z","timestamp":1760210940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/12\/457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,21]]},"references-count":42,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2016,12]]}},"alternative-id":["e18120457"],"URL":"https:\/\/doi.org\/10.3390\/e18120457","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,12,21]]}}}