{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T09:07:27Z","timestamp":1791277647684,"version":"4.1.0"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T00:00:00Z","timestamp":1326931200000},"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":[[2012,4]]},"abstract":"<jats:p>When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the<jats:italic>integrated covariation<\/jats:italic>(IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466611000326_inline1\"><jats:alt-text>$I\\hat C_n $<\/jats:alt-text><\/jats:inline-graphic>is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008,<jats:italic>Stochastic Processes and Their Applications<\/jats:italic>118, 517\u2013559), no assumptions on the volatilities\u2019 dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466611000326_inline2\"><jats:alt-text>$I\\hat C_n $<\/jats:alt-text><\/jats:inline-graphic>and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005,<jats:italic>Bernoulli<\/jats:italic>11, 359\u2013379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises\u2019 impact on data negligible.<\/jats:p>","DOI":"10.1017\/s0266466611000326","type":"journal-article","created":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T13:31:11Z","timestamp":1326979871000},"page":"249-273","source":"Crossref","is-referenced-by-count":67,"title":["IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS"],"prefix":"10.1017","volume":"28","author":[{"given":"Cecilia","family":"Mancini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabio","family":"Gobbi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2012,1,19]]},"reference":[{"key":"S0266466611000326_ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.10.005"},{"key":"S0266466611000326_ref27","unstructured":"Mancini C. (2010) Central Limit Theorem for Integrated Covariation Estimate in Bidimensional Asset Prices with Stochastic Volatility and Infinite Activity L\u00e9vy Jumps. Working paper, University of Florence."},{"key":"S0266466611000326_ref26","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2008.00622.x"},{"key":"S0266466611000326_ref25","first-page":"19","article-title":"Disentangling the jumps of the diffusion in a geometric jumping Brownian motion","volume":"64","author":"Mancini","year":"2001","journal-title":"Giornale dell\u2019Istituto Italiano degli Attuari"},{"key":"S0266466611000326_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.05.005"},{"key":"S0266466611000326_ref9","article-title":"Outlyingness weighted quadratic covariation","author":"Boudt","journal-title":"Journal of Financial Econometrics"},{"key":"S0266466611000326_ref18","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbi025"},{"key":"S0266466611000326_ref24","doi-asserted-by":"publisher","DOI":"10.1111\/0022-1082.00340"},{"key":"S0266466611000326_ref17","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1116340299"},{"key":"S0266466611000326_ref19","unstructured":"Jacod J. 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(2009) Dynamic Hedging of Portfolio Credit Derivatives. Working paper, available on www.ssrn.com.","DOI":"10.2139\/ssrn.1349847"},{"key":"S0266466611000326_ref4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00515.x"},{"key":"S0266466611000326_ref5","unstructured":"Barndorff-Nielsen O.E. & Shephard N. (2004b) Measuring the Impact of Jumps in Multivariate Price Processes Using Bipower Covariation. 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