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We suggest copulas for first\u2010order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co\u2010movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value\u2010at\u2010risk forecasts.<\/jats:p>","DOI":"10.1002\/jae.2610","type":"journal-article","created":{"date-parts":[[2017,11,7]],"date-time":"2017-11-07T09:08:41Z","timestamp":1510045721000},"page":"332-354","source":"Crossref","is-referenced-by-count":28,"title":["Time series copulas for heteroskedastic data"],"prefix":"10.1002","volume":"33","author":[{"given":"Rub\u00e9n","family":"Loaiza\u2010Maya","sequence":"first","affiliation":[{"name":"Melbourne Business School University of Melbourne  Melbourne, Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael S.","family":"Smith","sequence":"additional","affiliation":[{"name":"Melbourne Business School University of Melbourne  Melbourne, Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Worapree","family":"Maneesoonthorn","sequence":"additional","affiliation":[{"name":"Melbourne Business School University of Melbourne  Melbourne, Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2017,11,7]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2007.02.001"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2011.08.015"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/2298012"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500102753410390"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA8152"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466612000126"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/jtsa.12103"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1080.0669"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/937332.937333"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-1996(87)80025-9"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/asmb.2043"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0320-4"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA122"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.03.004"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS719"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2527341"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2379"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2015.03.027"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1255987328"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jempfin.2014.11.008"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1751-5823.2005.tb00254.x"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610910802645321"},{"key":"e_1_2_7_24_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618487"},{"key":"e_1_2_7_25_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009063"},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/isaf.216"},{"key":"e_1_2_7_27_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1197"},{"key":"e_1_2_7_28_1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/3.2.281"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.800"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609090720"},{"key":"e_1_2_7_31_1","doi-asserted-by":"publisher","DOI":"10.1201\/b13150"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.1201\/b17116"},{"key":"e_1_2_7_33_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2005.00173.x"},{"key":"e_1_2_7_34_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1249"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbp031"},{"key":"e_1_2_7_36_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00261.x"},{"key":"e_1_2_7_37_1","series-title":"Springer Series in Statistics","volume-title":"An Introduction to Copulas","author":"Nelsen R. 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