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Surprisingly, there have been few studies on this important issue, in spite of some ad hoc approaches to treat multiple transactions. In this paper we investigate how to handle multiple transactions, particularly in the context of estimating the integrated volatility and integrated quarticity, which are of great interest in financial econometrics. Two approaches are proposed for this purpose, and their asymptotic properties are investigated. Their performances are confirmed by simulation studies. The estimators are also applied to some real world problems. The work represents only the first step in this direction, and some future research problems are discussed.<\/jats:p>","DOI":"10.1017\/s0266466615000420","type":"journal-article","created":{"date-parts":[[2016,2,15]],"date-time":"2016-02-15T09:48:17Z","timestamp":1455529697000},"page":"331-365","source":"Crossref","is-referenced-by-count":8,"title":["ESTIMATING VOLATILITY FUNCTIONALS WITH MULTIPLE TRANSACTIONS"],"prefix":"10.1017","volume":"33","author":[{"given":"Bing-Yi","family":"Jing","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin-Bing","family":"Kong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,15]]},"reference":[{"key":"S0266466615000420_ref27","doi-asserted-by":"publisher","DOI":"10.1002\/0471746193"},{"key":"S0266466615000420_ref9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00515.x"},{"key":"S0266466615000420_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.09.036"},{"key":"S0266466615000420_ref6","volume-title":"From Stochastic Analysis to Mathematical Finance; 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