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This expression provides the first exact assessment of the impacts of nonstationarity, model complexity, and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.<\/jats:p>","DOI":"10.1017\/s0266466609990107","type":"journal-article","created":{"date-parts":[[2009,10,26]],"date-time":"2009-10-26T07:15:54Z","timestamp":1256541354000},"page":"774-803","source":"Crossref","is-referenced-by-count":10,"title":["PREDICTION ERRORS IN NONSTATIONARY AUTOREGRESSIONS OF INFINITE ORDER"],"prefix":"10.1017","volume":"26","author":[{"given":"Ching-Kang","family":"Ing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chor-yiu","family":"Sin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shu-Hui","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,10,26]]},"reference":[{"key":"S0266466609990107_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466609990107_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350711"},{"key":"S0266466609990107_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/074921706000000950"},{"key":"S0266466609990107_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1950-7"},{"key":"S0266466609990107_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S0047-259X(02)00029-5"},{"key":"S0266466609990107_ref8","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.2001.2063"},{"key":"S0266466609990107_ref19","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344897"},{"key":"S0266466609990107_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001550"},{"key":"S0266466609990107_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350617"},{"key":"S0266466609990107_ref4","volume-title":"Convergence of Probability Measure","author":"Billingsley","year":"1968"},{"key":"S0266466609990107_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/1999932"},{"key":"S0266466609990107_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342709"},{"key":"S0266466609990107_ref6","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1983.11971218"},{"key":"S0266466609990107_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1981.10477622"},{"key":"S0266466609990107_ref10","doi-asserted-by":"publisher","DOI":"10.1109\/18.165449"},{"key":"S0266466609990107_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603192031"},{"key":"S0266466609990107_ref14","unstructured":"Ing C.-K. , Sin C.-y. , & Yu S.-H. 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