{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,3]],"date-time":"2026-11-03T14:51:55Z","timestamp":1793717515556,"version":"4.6.1"},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T00:00:00Z","timestamp":1254268800000},"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":[[2010,4]]},"abstract":"<jats:p>\n                    Recently, Shimotsu and Phillips (2005,\n                    <jats:italic>Annals of Statistics<\/jats:italic>\n                    33, 1890\u20131933) developed a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the memory parameter (\n                    <jats:italic>d<\/jats:italic>\n                    ) in fractionally integrated processes. The ELW estimator has been shown to be consistent, and it has the same\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466609100075_eqi1\">\n                      <jats:alt-text>$N(0,{\\textstyle{1 \\over 4}})$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    asymptotic distribution for all values of\n                    <jats:italic>d<\/jats:italic>\n                    , if the optimization covers an interval of width less than 9\/2 and the mean of the process is known. With the intent to provide a semiparametric estimator suitable for economic data, we extend the ELW estimator so that it accommodates an unknown mean and a polynomial time trend. We show that the two-step ELW estimator, which is based on a modified ELW objective function using a tapered local Whittle estimator in the first stage, has an\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466609100075_eqi2\">\n                      <jats:alt-text>$N(0,{\\textstyle{1 \\over 4}})$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    asymptotic distribution for\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466609100075_eqi3\">\n                      <jats:alt-text>$d \\in (- {\\textstyle{1 \\over 2}},2)$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    (or\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466609100075_eqi4\">\n                      <jats:alt-text>$d \\in (- {\\textstyle{1 \\over 2}},{\\textstyle{7 \\over 4}})$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    when the data have a polynomial trend). Our simulation study illustrates that the two-step ELW estimator inherits the desirable properties of the ELW estimator.\n                  <\/jats:p>","DOI":"10.1017\/s0266466609100075","type":"journal-article","created":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T04:29:59Z","timestamp":1254284999000},"page":"501-540","source":"Crossref","is-referenced-by-count":188,"title":["EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND"],"prefix":"10.1017","volume":"26","author":[{"given":"Katsumi","family":"Shimotsu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,9,30]]},"reference":[{"key":"S0266466609100075_ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.09.014"},{"key":"S0266466609100075_ref32","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1988.tb00463.x"},{"key":"S0266466609100075_ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.08.015"},{"key":"S0266466609100075_ref30","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324317"},{"key":"S0266466609100075_ref29","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324636"},{"key":"S0266466609100075_ref26","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1214\/009053604000000139","article-title":"Local Whittle estimation in nonstationary and unit root cases","volume":"32","author":"Phillips","year":"2004","journal-title":"Annals of Statistics"},{"key":"S0266466609100075_ref25","first-page":"300","volume-title":"Essays in Memory of E.J. Hannan","author":"Phillips","year":"1996"},{"key":"S0266466609100075_ref23","first-page":"201","volume-title":"Proceedings of the Prague Symposium on Asymptotics","volume":"1","author":"Pfanzagl","year":"1974"},{"key":"S0266466609100075_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(98)00245-6"},{"key":"S0266466609100075_ref18","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1080\/07350015.2000.10524881","article-title":"Long memory in stock-market trading volume","volume":"18","author":"Lobato","year":"2000","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466609100075_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(98)00038-4"},{"key":"S0266466609100075_ref11","first-page":"419","volume-title":"Long-Range Dependence: Theory and Applications","author":"Henry","year":"2003"},{"key":"S0266466609100075_ref9","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/07350015.1995.10524577","article-title":"Long memory in inflation rates: International evidence","volume":"13","author":"Hassler","year":"1995","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466609100075_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/2109680"},{"key":"S0266466609100075_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1765(94)90025-6"},{"key":"S0266466609100075_ref4","doi-asserted-by":"publisher","DOI":"10.1162\/003465397556773"},{"key":"S0266466609100075_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.01.020"},{"key":"S0266466609100075_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3932(82)90012-5"},{"key":"S0266466609100075_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349666"},{"key":"S0266466609100075_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100009580"},{"key":"S0266466609100075_ref20","doi-asserted-by":"publisher","DOI":"10.1002\/jae.624"},{"key":"S0266466609100075_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342867"},{"key":"S0266466609100075_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2077735"},{"key":"S0266466609100075_ref12","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00179"},{"key":"S0266466609100075_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.017"},{"key":"S0266466609100075_ref28","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476881"},{"key":"S0266466609100075_ref33","doi-asserted-by":"publisher","DOI":"10.1002\/jae.3950060407"},{"key":"S0266466609100075_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/2110038"},{"key":"S0266466609100075_ref14","unstructured":"Kim C.S. & Phillips P.C.B. (2006) Log Periodogram Regression: The Nonstationary Case. Cowles Foundation Discussion paper 1587, Yale University."},{"key":"S0266466609100075_ref34","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000309"},{"key":"S0266466609100075_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3932(99)00045-8"},{"key":"S0266466609100075_ref16","first-page":"129","volume-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability","author":"LeCam","year":"1956"},{"key":"S0266466609100075_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00038-9"},{"key":"S0266466609100075_ref36","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00127"},{"key":"S0266466609100075_ref27","doi-asserted-by":"publisher","DOI":"10.2307\/1911699"},{"key":"S0266466609100075_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90104-Y"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466609100075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,16]],"date-time":"2024-03-16T17:05:51Z","timestamp":1710608751000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466609100075\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,30]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["S0266466609100075"],"URL":"https:\/\/doi.org\/10.1017\/s0266466609100075","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,30]]}}}