{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T08:13:04Z","timestamp":1789978384620,"version":"4.0.1"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2010,4,8]],"date-time":"2010-04-08T00:00:00Z","timestamp":1270684800000},"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":[[2010,12]]},"abstract":"<jats:p>Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466610000216_inline1\"><jats:alt-text>$(1 - L)^{ - d} &amp;#x003D; \\sum\\nolimits_{n &amp;#x003D; 0}^\\infty {b_n } L^n$<\/jats:alt-text><\/jats:inline-graphic>to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weights<jats:italic>b<jats:sub>n<\/jats:sub><\/jats:italic>decay at the rate<jats:italic>n<jats:sup>d<\/jats:sup><\/jats:italic><jats:sup>\u22121<\/jats:sup>and are not absolutely summable for long memory models (<jats:italic>d<\/jats:italic>&gt; 0). It has been believed that this rate is inherited by the impulse responses of any long memory fractionally integrated model. We show that this conjecture does not hold in such generality, and we establish a simple necessary and sufficient condition for the rate<jats:italic>n<jats:sup>d<\/jats:sup><\/jats:italic><jats:sup>\u22121<\/jats:sup>to be inherited by fractionally integrated processes.<\/jats:p>","DOI":"10.1017\/s0266466610000216","type":"journal-article","created":{"date-parts":[[2010,4,8]],"date-time":"2010-04-08T10:38:45Z","timestamp":1270723125000},"page":"1855-1861","source":"Crossref","is-referenced-by-count":28,"title":["IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY"],"prefix":"10.1017","volume":"26","author":[{"given":"Uwe","family":"Hassler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piotr","family":"Kokoszka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,4,8]]},"reference":[{"key":"S0266466610000216_ref17","volume-title":"Trigonometric Series","volume":"1","author":"Zygmund","year":"1959"},{"key":"S0266466610000216_ref16","volume-title":"Fourier Series","author":"Tolstov","year":"1976"},{"key":"S0266466610000216_ref13","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199257294.001.0001","volume-title":"Time Series with Long Memory","author":"Robinson","year":"2003"},{"key":"S0266466610000216_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-006-0074-4"},{"key":"S0266466610000216_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.03.006"},{"key":"S0266466610000216_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(98)00245-6"},{"key":"S0266466610000216_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(95)00034-8"},{"key":"S0266466610000216_ref5","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.165"},{"key":"S0266466610000216_ref4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1980.tb00297.x"},{"key":"S0266466610000216_ref15","volume-title":"Long Memory in Economics","author":"Teyssiere","year":"2006"},{"key":"S0266466610000216_ref2","volume-title":"Theory and Applications of Long Range Dependence","author":"Doukhan","year":"2003"},{"key":"S0266466610000216_ref12","volume-title":"Foundations of Time Series Analysis and Prediction Theory","author":"Pourahmadi","year":"2001"},{"key":"S0266466610000216_ref8","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1214\/aos\/1069362302","article-title":"Parameter estimation for infinite variance fractional ARIMA","volume":"24","author":"Kokoszka","year":"1996","journal-title":"Annals of Statistics"},{"key":"S0266466610000216_ref3","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1214\/aoap\/1019487516","article-title":"A model for long memory conditional heteroskedasticity","volume":"10","author":"Giraitis","year":"2000","journal-title":"Annals of Applied Probability"},{"key":"S0266466610000216_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.08.015"},{"key":"S0266466610000216_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.09.034"},{"key":"S0266466610000216_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(96)00124-X"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466610000216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T16:59:49Z","timestamp":1711385989000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466610000216\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,8]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0266466610000216"],"URL":"https:\/\/doi.org\/10.1017\/s0266466610000216","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4,8]]}}}