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We also discuss their covariance targeting specification and provide closed\u2010form formulas for multi\u2010step forecasts. Estimation and inference strategies are outlined. Empirical results suggest that the HEAVY model outperforms the multivariate GARCH model out\u2010of\u2010sample, with the gains being particularly significant at short forecast horizons. Forecast gains are obtained for both forecast variances and correlations. Copyright \u00a9 2011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.1260","type":"journal-article","created":{"date-parts":[[2011,8,4]],"date-time":"2011-08-04T16:31:07Z","timestamp":1312475467000},"page":"907-933","source":"Crossref","is-referenced-by-count":203,"title":["Multivariate high\u2010frequency\u2010based volatility (HEAVY) models"],"prefix":"10.1002","volume":"27","author":[{"given":"Diaa","family":"Noureldin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neil","family":"Shephard","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Sheppard","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2011,8,4]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500106000000332"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2527343"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00418"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest.89.4.701"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.032"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474930600713564"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00336"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00515.x"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA6495"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.07.009"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.021"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.842"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474939208800229"},{"key":"e_1_2_8_15_1","doi-asserted-by":"crossref","unstructured":"BrownleesCT EngleRF.2010.Volatility correlation and tails for systemic risk measurement. 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