{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T22:00:33Z","timestamp":1790805633618,"version":"4.1.0"},"reference-count":43,"publisher":"The Econometric Society","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high\u2010frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes, and data frequencies.<\/jats:p>","DOI":"10.3982\/ecta17505","type":"journal-article","created":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T08:18:21Z","timestamp":1642753101000},"page":"367-389","source":"Crossref","is-referenced-by-count":68,"title":["A ReMeDI for Microstructure Noise"],"prefix":"10.3982","volume":"90","author":[{"given":"Z. Merrick","family":"Li","sequence":"first","affiliation":[{"name":"Department of Economics, The Chinese University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oliver","family":"Linton","sequence":"additional","affiliation":[{"name":"Faculty of Economics, University of Cambridge"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2022]]},"reference":[{"key":"ecta200362-bib-0001","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1111\/j.1468-0262.2006.00655.x","volume":"74","author":"Abadie","year":"2006","journal-title":"Econometrica"},{"key":"ecta200362-bib-0002","volume-title":"High-Frequency Financial Econometrics","author":"A\u00eft-Sahalia","year":"2014"},{"key":"ecta200362-bib-0003","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1093\/rfs\/hhi016","volume":"18","author":"A\u00eft-Sahalia","year":"2005","journal-title":"Review of Financial Studies"},{"key":"ecta200362-bib-0004","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.jeconom.2010.03.028","volume":"160","author":"A\u00eft-Sahalia","year":"2011","journal-title":"Journal of Econometrics"},{"key":"ecta200362-bib-0005","author":"Andersen","year":"2020","journal-title":"Journal of Econometrics"},{"key":"ecta200362-bib-0006","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4j72","volume-title":"Mostly Harmless Econometrics: An Empiricist's Companion","author":"Angrist","year":"2008"},{"key":"ecta200362-bib-0007","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1111\/j.1467-937X.2008.00474.x","volume":"75","author":"Bandi","year":"2008","journal-title":"Review of Economic Studies"},{"key":"ecta200362-bib-0008","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA6495","volume":"76","author":"Barndorff-Nielsen","year":"2008","journal-title":"Econometrica"},{"key":"ecta200362-bib-0009","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1111\/j.1540-6261.1995.tb05192.x","volume":"50","author":"Biais","year":"1995","journal-title":"Journal of Finance"},{"key":"ecta200362-bib-0010","doi-asserted-by":"crossref","first-page":"219","DOI":"10.2307\/2330882","volume":"23","author":"Choi","year":"1988","journal-title":"Journal of Financial and Quantitative Analysis"},{"key":"ecta200362-bib-0011","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.jfineco.2014.07.007","volume":"114","author":"Christensen","year":"2014","journal-title":"Journal of Financial Economics"},{"key":"ecta200362-bib-0012","unstructured":"Da, R., and D. Xiu (2019): \u201cWhen Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility,\u201d Tech. rep."},{"key":"ecta200362-bib-0013","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/3318650","author":"Delattre","year":"1997","journal-title":"Bernoulli"},{"key":"ecta200362-bib-0014","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BF01450498","volume":"300","author":"Delbaen","year":"1994","journal-title":"Mathematische Annalen"},{"key":"ecta200362-bib-0015","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0304-405X(86)90004-8","volume":"17","author":"French","year":"1986","journal-title":"Journal of Financial Economics"},{"key":"ecta200362-bib-0016","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0304-405X(88)90034-7","volume":"21","author":"Glosten","year":"1988","journal-title":"Journal of Financial Economics"},{"key":"ecta200362-bib-0017","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1017\/S0266466613000121","author":"Hansen","year":"2014","journal-title":"Econometric Theory"},{"key":"ecta200362-bib-0018","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195301649.001.0001","volume-title":"Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading","author":"Hasbrouck","year":"2007"},{"key":"ecta200362-bib-0019","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1111\/j.1540-6261.1987.tb03926.x","volume":"42","author":"Hasbrouck","year":"1987","journal-title":"Journal of Finance"},{"key":"ecta200362-bib-0020","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.jfineco.2014.08.001","volume":"114","author":"Hendershott","year":"2014","journal-title":"Journal of Financial Economics"},{"key":"ecta200362-bib-0021","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0304-405X(81)90020-9","volume":"9","author":"Ho","year":"1981","journal-title":"Journal of Financial Economics"},{"key":"ecta200362-bib-0022","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1093\/rfs\/10.4.995","volume":"10","author":"Huang","year":"1997","journal-title":"Review of Financial Studies"},{"key":"ecta200362-bib-0023","volume-title":"Discretization of Processes","volume":"67","author":"Jacod","year":"2011"},{"key":"ecta200362-bib-0024","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05265-5","volume-title":"Limit Theorems for Stochastic Processes","volume":"288","author":"Jacod","year":"2003"},{"key":"ecta200362-bib-0025","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1016\/j.spa.2008.11.004","volume":"119","author":"Jacod","year":"2009","journal-title":"Stochastic Processes and their Applications"},{"key":"ecta200362-bib-0026","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.3982\/ECTA13085","volume":"85","author":"Jacod","year":"2017","journal-title":"Econometrica"},{"key":"ecta200362-bib-0027","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2937816","volume":"105","author":"Lehmann","year":"1990","journal-title":"Quarterly Journal of Economics"},{"key":"ecta200362-bib-0028","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.3982\/ECTA10534","volume":"81","author":"Li","year":"2013","journal-title":"Econometrica"},{"key":"ecta200362-bib-0029","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1093\/jjfinec\/nbu005","volume":"13","author":"Li","year":"2015","journal-title":"Journal of Financial Econometrics"},{"key":"ecta200362-bib-0030","doi-asserted-by":"crossref","unstructured":"Li, Z. M., and O. Linton (2019): \u201cA ReMeDI for Microstructure Noise,\u201d https:\/\/ssrn.com\/abstract=3423607.","DOI":"10.2139\/ssrn.3423607"},{"key":"ecta200362-bib-0031","doi-asserted-by":"crossref","unstructured":"Li, Z. M., O. Linton (2022): \u201cSupplement to \u2018A ReMeDI for Microstructure Noise\u2019,\u201d Econometrica Supplemental Material, 90, https:\/\/doi.org\/10.3982\/ECTA17505.","DOI":"10.3982\/ECTA17505"},{"key":"ecta200362-bib-0032","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.jeconom.2019.10.004","volume":"215","author":"Li","year":"2020","journal-title":"Journal of Econometrics"},{"key":"ecta200362-bib-0033","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1146\/annurev-economics-063016-104407","volume":"10","author":"Linton","year":"2018","journal-title":"Annual Review of Economics"},{"key":"ecta200362-bib-0034","volume-title":"Market Microstructure Theory","volume":"108","author":"O'Hara","year":"1995"},{"key":"ecta200362-bib-0035","doi-asserted-by":"crossref","first-page":"973","DOI":"10.3982\/ECTA8602","volume":"79","author":"Park","year":"2011","journal-title":"Econometrica"},{"key":"ecta200362-bib-0036","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1093\/rfs\/11.4.789","volume":"11","author":"Parlour","year":"1998","journal-title":"Review of Financial Studies"},{"key":"ecta200362-bib-0037","doi-asserted-by":"crossref","first-page":"687","DOI":"10.3150\/08-BEJ170","volume":"15","author":"Rosenbaum","year":"2009","journal-title":"Bernoulli"},{"key":"ecta200362-bib-0038","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1111\/j.1540-6261.1977.tb03240.x","volume":"32","author":"Schwartz","year":"1977","journal-title":"Journal of Finance"},{"key":"ecta200362-bib-0039","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1016\/j.spa.2013.04.005","volume":"123","author":"Todorov","year":"2013","journal-title":"Stochastic Processes and their Applications"},{"key":"ecta200362-bib-0040","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1198\/jbes.2010.08342","volume":"29","author":"Todorov","year":"2011","journal-title":"Journal of Business & Economic Statistics"},{"key":"ecta200362-bib-0041","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.jeconom.2010.07.002","volume":"159","author":"Xiu","year":"2010","journal-title":"Journal of Econometrics"},{"key":"ecta200362-bib-0042","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.3150\/bj\/1165269149","volume":"12","author":"Zhang","year":"2006","journal-title":"Bernoulli"},{"key":"ecta200362-bib-0043","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1198\/016214505000000169","volume":"100","author":"Zhang","year":"2005","journal-title":"Journal of the American Statistical Association"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T02:27:13Z","timestamp":1700101633000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA17505"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022]]}},"alternative-id":["10.3982\/ECTA17505"],"URL":"https:\/\/doi.org\/10.3982\/ecta17505","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2022]]}}}