{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T14:12:14Z","timestamp":1790518334687,"version":"4.1.0"},"reference-count":64,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2016,12,8]],"date-time":"2016-12-08T00:00:00Z","timestamp":1481155200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>This paper analyzes a generalized class of flat-top realized kernel estimators for the quadratic variation spectrum, that is, the decomposition of quadratic variation into integrated variance and jump variation. The underlying log-price process is contaminated by additive noise, which consists of two orthogonal components to accommodate <jats:italic>\u03b1<\/jats:italic>-mixing dependent exogenous noise and an asymptotically non-degenerate endogenous correlation structure. In the absence of jumps, the class of estimators is shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, <jats:italic>n<\/jats:italic><jats:sup>1\/4<\/jats:sup>. Exact bounds on lower-order terms are obtained, and these are used to propose a selection rule for the flat-top shrinkage. Bounds on the optimal bandwidth for noise models of varying complexity are also provided. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a bias-corrected pre-averaging estimator, the flat-top realized kernel enjoys a higher-order advantage in terms of bias reduction, in addition to good efficiency properties. The analysis is extended to jump-diffusions where the asymptotic properties of a flat-top realized kernel estimate of the total quadratic variation are established. Apart from a larger asymptotic variance, they are similar to the no-jump case. Finally, the estimators are used to design two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have no loss either of asymptotic efficiency or in the rate of consistency relative to the flat-top realized kernels when jumps are absent. However, only the medium blocked realized kernels achieve the optimal rate of convergence under the jump alternative.<\/jats:p>","DOI":"10.1017\/s0266466616000475","type":"journal-article","created":{"date-parts":[[2016,12,8]],"date-time":"2016-12-08T07:06:06Z","timestamp":1481180766000},"page":"1457-1501","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":33,"title":["ESTIMATING THE QUADRATIC VARIATION SPECTRUM OF NOISY ASSET PRICES USING GENERALIZED FLAT-TOP REALIZED KERNELS"],"prefix":"10.1017","volume":"33","author":[{"given":"Rasmus Tangsgaard","family":"Varneskov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,12,8]]},"reference":[{"key":"S0266466616000475_ref6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/B978-0-444-50897-3.50005-5","volume-title":"Handbook of Financial Econometrics","author":"Andersen","year":"2010"},{"key":"S0266466616000475_ref40","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1214\/aop\/1022855419","article-title":"Asymptotic error distributions for the euler method for stochastic differential equations","volume":"26","author":"Jacod","year":"1998","journal-title":"Annals of Probability"},{"key":"S0266466616000475_ref30","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0304-405X(85)90044-3","article-title":"Bid, ask and transaction prices in a specialist market with heterogeneously informed traders","volume":"14","author":"Glosten","year":"1985","journal-title":"Journal of Financial Economics"},{"key":"S0266466616000475_ref15","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jeconom.2010.07.009","article-title":"Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading","volume":"162","author":"Barndorff-Nielsen","year":"2011a","journal-title":"Journal of Econometrics"},{"key":"S0266466616000475_ref13","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA6495","article-title":"Designing realized kernels to measure the ex-post variation of equity prices in the presence of noise","volume":"76","author":"Barndorff-Nielsen","year":"2008","journal-title":"Econometrica"},{"key":"S0266466616000475_ref25","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1111\/1467-9965.00057","article-title":"Long memory in continuous-time stochastic volatility models","volume":"8","author":"Comte","year":"1998","journal-title":"Mathematical Finance"},{"key":"S0266466616000475_ref22","doi-asserted-by":"crossref","unstructured":"Brillinger, D.R . 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