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Several applications of the results are given, relevant for the theories of estimation with <jats:italic>I<\/jats:italic>(1) processes, <jats:italic>I<\/jats:italic>(2) processes, processes with nonstationary variances, near-integrated processes, and continuous time approximations.<\/jats:p>","DOI":"10.1017\/s0266466600013189","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:15:30Z","timestamp":1287393330000},"page":"489-500","source":"Crossref","is-referenced-by-count":222,"title":["Convergence to Stochastic Integrals for Dependent Heterogeneous Processes"],"prefix":"10.1017","volume":"8","author":[{"given":"Bruce E.","family":"Hansen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600013189_ref010","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176990334"},{"key":"S0266466600013189_ref023","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012032"},{"key":"S0266466600013189_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(88)90039-5"},{"key":"S0266466600013189_ref020","doi-asserted-by":"publisher","DOI":"10.2307\/1911357"},{"key":"S0266466600013189_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90103-X"},{"key":"S0266466600013189_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013396"},{"key":"S0266466600013189_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466600013189_ref019","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001344X"},{"key":"S0266466600013189_ref015","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004436"},{"key":"S0266466600013189_ref008","first-page":"321","article-title":"Tests for parameter instability in regressions with 1(1) processes","volume":"10","author":"Hansen","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466600013189_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012287"},{"key":"S0266466600013189_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/BF00343897"},{"key":"S0266466600013189_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004485"},{"key":"S0266466600013189_ref002","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466600013189_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350711"},{"key":"S0266466600013189_ref005","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466600013189_ref007","unstructured":"7. Hansen B.E. Regression theory when variances are nonstationary. 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