{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:16:44Z","timestamp":1768724204758,"version":"3.49.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"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":[[2009,12]]},"abstract":"<jats:p>This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process\u2014possibly itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analyzed in a previous paper (Davidson and Hashimzade, 2008), and the construction derived from moving average representations in the time domain. Depending on the values of the long memory parameters and choice of normalization, the limiting integral is shown to be expressible as the sum of a constant and two It\u00f4-type integrals with respect to distinct Brownian motions. In certain cases the latter terms are of small order relative to the former. The mean is shown to match that of the harmonic representation, where the latter is defined, and satisfies the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulas are valid for the full range of the long memory parameters and that they extend to non-Gaussian processes.<\/jats:p>","DOI":"10.1017\/s0266466609990260","type":"journal-article","created":{"date-parts":[[2009,10,26]],"date-time":"2009-10-26T10:57:29Z","timestamp":1256554649000},"page":"1589-1624","source":"Crossref","is-referenced-by-count":7,"title":["REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES"],"prefix":"10.1017","volume":"25","author":[{"given":"James","family":"Davidson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nigar","family":"Hashimzade","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,12,1]]},"reference":[{"key":"S0266466609990260_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466609990260_ref13","doi-asserted-by":"publisher","DOI":"10.1111\/0022-1082.00347"},{"key":"S0266466609990260_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/2938278"},{"key":"S0266466609990260_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/2297545"},{"key":"S0266466609990260_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080110"},{"key":"S0266466609990260_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600165028"},{"key":"S0266466609990260_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.06.012"},{"key":"S0266466609990260_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/2938213"},{"key":"S0266466609990260_ref14","doi-asserted-by":"publisher","DOI":"10.1137\/1010093"},{"key":"S0266466609990260_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/0198774036.001.0001"},{"key":"S0266466609990260_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176990334"},{"key":"S0266466609990260_ref12","first-page":"1","volume-title":"Probabilistic Models for Nonlinear Partial Differential Equations: Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo","author":"Kurtz","year":"1996"},{"key":"S0266466609990260_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600165016"},{"key":"S0266466609990260_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004217"},{"key":"S0266466609990260_ref1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1972"},{"key":"S0266466609990260_ref4","unstructured":"Davidson J. . (2001) Addendum to \u201cThe functional central limit theorem and convergence to stochastic integrals II: fractionally integrated processes.\u201d Available at http:\/\/www.people.ex.ac.uk\/jehd201\/fcltfiadd.pdf."},{"key":"S0266466609990260_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324318"},{"key":"S0266466609990260_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005843"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466609990260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T17:54:44Z","timestamp":1555005284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466609990260\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":18,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["S0266466609990260"],"URL":"https:\/\/doi.org\/10.1017\/s0266466609990260","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}