{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T08:41:11Z","timestamp":1793090471410,"version":"4.5.0"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2013,11,27]],"date-time":"2013-11-27T00:00:00Z","timestamp":1385510400000},"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":[[2014,6]]},"abstract":"<jats:p>When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the realized volatility in a general endogenous time setting. We also establish a central limit theorem for the tricity under the hypothesis that there is no endogeneity, based on which we propose a test and document that this endogeneity is present in financial data.<\/jats:p>","DOI":"10.1017\/s0266466613000418","type":"journal-article","created":{"date-parts":[[2013,11,27]],"date-time":"2013-11-27T08:58:48Z","timestamp":1385542728000},"page":"580-605","source":"Crossref","is-referenced-by-count":72,"title":["REALIZED VOLATILITY WHEN SAMPLING TIMES ARE POSSIBLY ENDOGENOUS"],"prefix":"10.1017","volume":"30","author":[{"given":"Yingying","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Per A.","family":"Mykland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Renault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinghua","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,11,27]]},"reference":[{"key":"S0266466613000418_ref12","doi-asserted-by":"crossref","unstructured":"Davison A.C. & Hinkley D.V. (1997) Bootstrap Methods and their Application, vol. 1 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, with 1 IBM-PC floppy disk (3.5 inch; HD).","DOI":"10.1017\/CBO9780511802843"},{"key":"S0266466613000418_ref54","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000169"},{"key":"S0266466613000418_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.02.006"},{"key":"S0266466613000418_ref39","unstructured":"Phillips P.C.B. & Yu J. (2007) Information Loss in Volatility Measurement with Flat Price Trading. Working paper."},{"key":"S0266466613000418_ref41","doi-asserted-by":"crossref","unstructured":"Renault E. , Van der Heijden T. , & Werker B.J. (2012) The Dynamic Mixed Hitting-Time Model for Multiple Transaction Prices and Times. Working paper.","DOI":"10.2139\/ssrn.2146220"},{"key":"S0266466613000418_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060324"},{"key":"S0266466613000418_ref14","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00553.x"},{"key":"S0266466613000418_ref23","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1116340299"},{"key":"S0266466613000418_ref45","doi-asserted-by":"publisher","DOI":"10.1137\/090764578"},{"key":"S0266466613000418_ref49","doi-asserted-by":"crossref","unstructured":"Wang D.C. & Mykland P.A. (2011) The Estimation of Leverage Effect with High Frequency Data. Working paper, University of Oxford.","DOI":"10.2139\/ssrn.1919138"},{"key":"S0266466613000418_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/11-AIHP432"},{"key":"S0266466613000418_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05265-5"},{"key":"S0266466613000418_ref19","doi-asserted-by":"crossref","unstructured":"Fukasawa M. & Rosenbaum M. (2012) Central limit theorems for realized volatility under hitting times of an irregular grid. Stochastic Processes and Their Applications, forthcoming.","DOI":"10.1016\/j.spa.2012.08.005"},{"key":"S0266466613000418_ref34","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325355"},{"key":"S0266466613000418_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-008-0087-3"},{"key":"S0266466613000418_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995577"},{"key":"S0266466613000418_ref16","doi-asserted-by":"crossref","unstructured":"Fan J. , Li Y. , & Yu K. (2010) Vast volatility Matrix Estimation using High Frequency Data for Portfolio Selection. (to appear in Journal of the American Statistical Association).","DOI":"10.2139\/ssrn.1596965"},{"key":"S0266466613000418_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.07.009"},{"key":"S0266466613000418_ref4","doi-asserted-by":"publisher","DOI":"10.2307\/2951771"},{"key":"S0266466613000418_ref7","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA6495","article-title":"Designing realized kernels to measure ex-post variation of equity prices in the presence of noise","volume":"76","author":"Barndorff-Nielsen","year":"2008","journal-title":"Econometrica"},{"key":"S0266466613000418_ref21","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466613000418_ref38","doi-asserted-by":"publisher","DOI":"10.1201\/b12126-3"},{"key":"S0266466613000418_ref47","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994774"},{"key":"S0266466613000418_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30788-4_3"},{"key":"S0266466613000418_ref24","unstructured":"Jacod J . (1994) Limit of Random Measures Associated with the Increments of a Brownian Semimartingale. Technical report, Universit\u00e9 de Paris VI."},{"key":"S0266466613000418_ref36","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000452"},{"key":"S0266466613000418_ref13","volume-title":"Probabilities and Potential B","author":"Dellacherie","year":"1982"},{"key":"S0266466613000418_ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.07.002"},{"key":"S0266466613000418_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbh001"},{"key":"S0266466613000418_ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.012"},{"key":"S0266466613000418_ref9","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00336"},{"key":"S0266466613000418_ref35","doi-asserted-by":"crossref","unstructured":"Mykland P.A. , Shephard N. , & Sheppard K. (2012) Efficient and feasible inference for the components of financial variation using blocked multipower variation. Working paper, University of Oxford.","DOI":"10.2139\/ssrn.2008690"},{"key":"S0266466613000418_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609090616"},{"key":"S0266466613000418_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00282"},{"key":"S0266466613000418_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.t01-1-00416"},{"key":"S0266466613000418_ref40","volume-title":"Stochastic Integration and Differential Equations: A New Approach","author":"Protter","year":"2004"},{"key":"S0266466613000418_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.11.004"},{"key":"S0266466613000418_ref26","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":"S0266466613000418_ref43","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660808047X"},{"key":"S0266466613000418_ref1","doi-asserted-by":"crossref","first-page":"783","DOI":"10.3982\/ECTA7312","article-title":"Mixed hitting-time models","volume":"80","author":"Abbring","year":"2012","journal-title":"Econometrica"},{"key":"S0266466613000418_ref11","doi-asserted-by":"crossref","unstructured":"Christensen K. , Podolskij M. , & Vetter M. (2011) On covariation estimation for multivariate continuous Ito semimartingales with noise in non-synchronous observation schemes. Working paper.","DOI":"10.2139\/ssrn.2050642"},{"key":"S0266466613000418_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00105-1"},{"key":"S0266466613000418_ref32","first-page":"19","article-title":"Disentangling the jumps of the diffusion in a geometric jumping Brownian motion","author":"Mancini","year":"2001","journal-title":"Giornale dell\u2019Istituto Italiano degli Attuari"},{"key":"S0266466613000418_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.036"},{"key":"S0266466613000418_ref37","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.3982\/ECTA7417","article-title":"Inference for continuous semimartingales observed at high frequency","volume":"77","author":"Mykland","year":"2009","journal-title":"Econometrica"},{"key":"S0266466613000418_ref44","first-page":"293","article-title":"On stable sequences of events","volume":"25","author":"R\u00e9nyi","year":"1963","journal-title":"Sanky\u0101 Series A"},{"key":"S0266466613000418_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2005.07.027"},{"key":"S0266466613000418_ref30","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhm056"},{"key":"S0266466613000418_ref48","volume-title":"Stochastic Processes","author":"Ross","year":"1996"},{"key":"S0266466613000418_ref52","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1165269149"},{"key":"S0266466613000418_ref46","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2010.00454.x"},{"key":"S0266466613000418_ref51","unstructured":"Zhang L . (2001) From Martingales to ANOVA: Implied and Realized Volatility. Ph.D. thesis, The University of Chicago."},{"key":"S0266466613000418_ref31","doi-asserted-by":"crossref","unstructured":"Li Y. , Zhang Z. , & Zheng X. (2013) Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise. A Special Issue on the Occasion of the 2013 International Year of Statistics (R. Dahlhaus, J. Jacod, P. Mykland, & N. Yoshida eds.), Stochastic Processes and their Applications, 123(7), 2696\u20132727.","DOI":"10.1016\/j.spa.2013.04.002"},{"key":"S0266466613000418_ref15","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00091"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466613000418","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,4]],"date-time":"2019-08-04T01:02:40Z","timestamp":1564880560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466613000418\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,27]]},"references-count":54,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S0266466613000418"],"URL":"https:\/\/doi.org\/10.1017\/s0266466613000418","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,27]]}}}