{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:25:25Z","timestamp":1769214325010,"version":"3.49.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2000,10,5]],"date-time":"2000-10-05T00:00:00Z","timestamp":970704000000},"content-version":"unspecified","delay-in-days":4,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2000,10]]},"abstract":"<jats:p>This paper derives a functional central limit theorem \nfor the partial sums of fractionally integrated processes, \notherwise known as <jats:italic>I<\/jats:italic>(<jats:italic>d<\/jats:italic>) processes \nfor |<jats:italic>d<\/jats:italic>| &lt; 1\/2. Such processes \nhave long memory, and the limit distribution is the \nso-called fractional Brownian motion, having correlated \nincrements even asymptotically. The underlying shock variables \nmay themselves exhibit quite general weak dependence by \nbeing near-epoch-dependent functions of mixing processes. \nSeveral weak convergence results for stochastic integrals \nhaving fractional integrands and weakly dependent integrators \nare also obtained. Taken together, these results permit \n<jats:italic>I<\/jats:italic>(<jats:italic>p<\/jats:italic> + <jats:italic>d<\/jats:italic>) integrands for any integer \n<jats:italic>p<\/jats:italic> \u2265 1.<\/jats:p>","DOI":"10.1017\/s0266466600165028","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:45:46Z","timestamp":1027777546000},"page":"643-666","source":"Crossref","is-referenced-by-count":68,"title":["THE FUNCTIONAL CENTRAL LIMIT THEOREM AND WEAK CONVERGENCE TO STOCHASTIC \nINTEGRALS II"],"prefix":"10.1017","volume":"16","author":[{"given":"James","family":"Davidson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert M.","family":"de Jong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2000,10,5]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600165028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T20:13:29Z","timestamp":1557346409000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600165028\/type\/journal_article"}},"subtitle":["Fractionally Integrated Processes"],"short-title":[],"issued":{"date-parts":[[2000,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2000,10]]}},"alternative-id":["S0266466600165028"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600165028","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,10]]}}}