{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:40:28Z","timestamp":1758400828336},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T00:00:00Z","timestamp":1243814400000},"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":[[2009,6]]},"abstract":"<jats:p>Standardized slowly varying regressors are shown to be <jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.<\/jats:p>","DOI":"10.1017\/s0266466608090282","type":"journal-article","created":{"date-parts":[[2009,5,26]],"date-time":"2009-05-26T13:32:22Z","timestamp":1243344742000},"page":"748-763","source":"Crossref","is-referenced-by-count":5,"title":["CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: <i>L<sub>P<\/sub><\/i> -APPROXIMABILITY VERSUS BROWNIAN MOTION"],"prefix":"10.1017","volume":"25","author":[{"given":"Kairat T.","family":"Mynbaev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,6,1]]},"reference":[{"key":"S0266466608090282_ref11","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0723"},{"key":"S0266466608090282_ref17","volume-title":"Time Series Analysis","author":"Tanaka","year":"1996"},{"key":"S0266466608090282_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(86)90102-X"},{"key":"S0266466608090282_ref15","doi-asserted-by":"publisher","DOI":"10.1080\/07474939108800204"},{"key":"S0266466608090282_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600165016"},{"key":"S0266466608090282_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(79)90050-4"},{"key":"S0266466608090282_ref1","first-page":"15","article-title":"Deux th\u00e9or\u00e8mes relatifs au comportement asymptotique des s\u00e9ries trigonom\u00e9triques","volume":"43","author":"Aljan\u010di\u0107","year":"1955","journal-title":"Zbornik Radova Matemati\u010dki Institut SANU"},{"key":"S0266466608090282_ref2","volume-title":"The Statistical Analysis of Time Series","author":"Anderson","year":"1971"},{"key":"S0266466608090282_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3932(81)90040-4"},{"key":"S0266466608090282_ref7","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466608090282_ref5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1214\/aop\/1042644709","article-title":"Second-order regular variation and rates of convergence in extreme-value theory","volume":"24","author":"de Haan","year":"1996","journal-title":"Annals of Probability"},{"key":"S0266466608090282_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316429"},{"key":"S0266466608090282_ref10","unstructured":"Moussatat M.W . (1976) On the asymptotic theory of statistical experiments and some of its applications. Ph.D. Dissertation, University of California, Berkeley."},{"key":"S0266466608090282_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2007.04.002"},{"key":"S0266466608090282_ref13","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466607070260"},{"key":"S0266466608090282_ref16","author":"Seneta","year":"1985"},{"key":"S0266466608090282_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348666"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090282","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T18:55:33Z","timestamp":1554317733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090282\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["S0266466608090282"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090282","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}