{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T08:01:54Z","timestamp":1790236914172,"version":"4.1.0"},"reference-count":49,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T00:00:00Z","timestamp":1243814400000},"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":[[2009,6]]},"abstract":"<jats:p>We establish sufficient conditions on durations that are stationary with finite variance and memory parameter<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466608090294_eqi1\"><jats:alt-text>$d \\in [0,{\\textstyle{1 \\over 2}})$<\/jats:alt-text><\/jats:inline-graphic>to ensure that the corresponding counting process<jats:italic>N<\/jats:italic>(<jats:italic>t<\/jats:italic>) satisfies Var<jats:italic>N<\/jats:italic>(<jats:italic>t<\/jats:italic>) ~<jats:italic>Ct<\/jats:italic><jats:sup>2<jats:italic>d<\/jats:italic>+1<\/jats:sup>(<jats:italic>C<\/jats:italic>&gt; 0) as<jats:italic>t<\/jats:italic>\u2192 \u221e, with the same memory parameter<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466608090294_eqi2\"><jats:alt-text>$d \\in [0,{\\textstyle{1 \\over 2}})$<\/jats:alt-text><\/jats:inline-graphic>that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the counts. We then show that any autoregressive conditional duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, whereas any long memory stochastic duration model with<jats:italic>d<\/jats:italic>&gt; 0 and all finite moments yields long memory in counts, with the same<jats:italic>d<\/jats:italic>. Finally, we provide some results about the propagation of long memory to the empirically relevant case of realized variance estimates affected by market microstructure noise contamination.<\/jats:p>","DOI":"10.1017\/s0266466608090294","type":"journal-article","created":{"date-parts":[[2009,5,26]],"date-time":"2009-05-26T13:32:22Z","timestamp":1243344742000},"page":"764-792","source":"Crossref","is-referenced-by-count":27,"title":["CONDITIONS FOR THE PROPAGATION OF MEMORY PARAMETER FROM DURATIONS TO COUNTS AND REALIZED VOLATILITY"],"prefix":"10.1017","volume":"25","author":[{"given":"Rohit","family":"Deo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Clifford M.","family":"Hurvich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe","family":"Soulier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,6,1]]},"reference":[{"key":"S0266466608090294_ref48","doi-asserted-by":"publisher","DOI":"10.1007\/BF00534186"},{"key":"S0266466608090294_ref47","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1995.tb00237.x"},{"key":"S0266466608090294_ref46","doi-asserted-by":"publisher","DOI":"10.1002\/0471264105"},{"key":"S0266466608090294_ref45","doi-asserted-by":"publisher","DOI":"10.2307\/1912002"},{"key":"S0266466608090294_ref44","first-page":"311","article-title":"Long memory properties and covariance structure of the EGARCH model","volume":"6","author":"Surgailis","year":"2002","journal-title":"European Series in Applied and Industrial Mathematics: Probability and Statistics"},{"key":"S0266466608090294_ref43","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbg002"},{"key":"S0266466608090294_ref42","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1984.tb03897.x"},{"key":"S0266466608090294_ref40","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90078-R"},{"key":"S0266466608090294_ref39","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1069362376"},{"key":"S0266466608090294_ref38","doi-asserted-by":"publisher","DOI":"10.1086\/294980"},{"key":"S0266466608090294_ref37","doi-asserted-by":"publisher","DOI":"10.1198\/073500106000000044"},{"key":"S0266466608090294_ref33","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693249"},{"key":"S0266466608090294_ref32","volume-title":"Independent and Stationary Sequences of Random Variables","author":"Ibragimov","year":"1971"},{"key":"S0266466608090294_ref31","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00616.x"},{"key":"S0266466608090294_ref29","doi-asserted-by":"publisher","DOI":"10.1198\/073500106000000071"},{"key":"S0266466608090294_ref27","doi-asserted-by":"publisher","DOI":"10.2307\/2999632"},{"key":"S0266466608090294_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.06.002"},{"key":"S0266466608090294_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00089-1"},{"key":"S0266466608090294_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800010454"},{"key":"S0266466608090294_ref36","doi-asserted-by":"publisher","DOI":"10.1007\/BF00367306"},{"key":"S0266466608090294_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/1913889"},{"key":"S0266466608090294_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.01.003"},{"key":"S0266466608090294_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.01.009"},{"key":"S0266466608090294_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2642-0"},{"key":"S0266466608090294_ref30","first-page":"307","volume-title":"Forecasting Volatility in Financial Markets","author":"Harvey","year":"1998"},{"key":"S0266466608090294_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11657-9"},{"key":"S0266466608090294_ref49","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000169"},{"key":"S0266466608090294_ref3","volume-title":"Introductory Graph Theory","author":"Andrasfai","year":"1977"},{"key":"S0266466608090294_ref9","volume-title":"Probability and Measure","author":"Billingsley","year":"1986"},{"key":"S0266466608090294_ref20","volume-title":"An Introduction to the Theory of Point Processes","author":"Daley","year":"2003"},{"key":"S0266466608090294_ref41","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466699153027"},{"key":"S0266466608090294_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466608090294_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2005.01.005"},{"key":"S0266466608090294_ref28","doi-asserted-by":"publisher","DOI":"10.2307\/1912726"},{"key":"S0266466608090294_ref34","doi-asserted-by":"crossref","unstructured":"Jasiak J . 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