{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T23:32:20Z","timestamp":1720654340126},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"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":[[2009,4]]},"abstract":"<jats:p>Lai and Wei (1983, <jats:italic>Annals of Statistics<\/jats:italic> 10, 154\u2013166) state in their Theorem 1 that the estimators of the regression coefficients in the regression <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466608090579_eqi1\"><jats:alt-text>$y_t  = x_t^' \\beta  + \\varepsilon _{\\rm{t}} $<\/jats:alt-text><\/jats:inline-graphic>, <jats:italic>t<\/jats:italic> \u2208 \u2115 are almost surely (a.s.) consistent under the assumption that the minimum eigenvalue <jats:italic>\u03bb<jats:sub>min<\/jats:sub><\/jats:italic>(<jats:italic>T<\/jats:italic>) of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466608090579_eqi2\"><jats:alt-text>$\\sum\\nolimits_{t &amp;#x003D; 1}^T {x_t } x&amp;#x0027;_t $<\/jats:alt-text><\/jats:inline-graphic> tends to infinity (a.s.) and log(<jats:italic>\u03bb<jats:sub>max<\/jats:sub><\/jats:italic>(<jats:italic>T<\/jats:italic>))\/<jats:italic>\u03bb<jats:sub>min<\/jats:sub><\/jats:italic>(<jats:italic>T<\/jats:italic>) \u2192 0 (a.s.) where <jats:italic>\u03bb<jats:sub>max<\/jats:sub><\/jats:italic>(<jats:italic>T<\/jats:italic>) denotes the maximal eigenvalue. Moreover the rate of convergence in this case equals <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466608090579_eqi3\"><jats:alt-text>$O(\\root  \\of {\\log (\\lambda _{max} (T))\/\\lambda _{min} (T)})$<\/jats:alt-text><\/jats:inline-graphic>. In this note <jats:italic>x<jats:sub>t<\/jats:sub><\/jats:italic> is taken to be a particular multivariate multifrequency I(1) processes, and almost sure rates of convergence for least squares estimators are established.<\/jats:p>","DOI":"10.1017\/s0266466608090579","type":"journal-article","created":{"date-parts":[[2009,1,30]],"date-time":"2009-01-30T09:50:05Z","timestamp":1233309005000},"page":"571-582","source":"Crossref","is-referenced-by-count":2,"title":["ALMOST SURE BOUNDS ON THE ESTIMATION ERROR FOR OLS ESTIMATORS WHEN THE REGRESSORS INCLUDE CERTAIN MFI(1) PROCESSES"],"prefix":"10.1017","volume":"25","author":[{"given":"Dietmar","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,4,1]]},"reference":[{"key":"S0266466608090579_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050310"},{"key":"S0266466608090579_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(83)90002-7"},{"key":"S0266466608090579_ref3","volume-title":"Linear Systems","author":"Kailath","year":"1980"},{"key":"S0266466608090579_ref2","volume-title":"The Statistical Theory of Linear Systems","author":"Hannan","year":"1988"},{"key":"S0266466608090579_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345697"},{"key":"S0266466608090579_ref1","unstructured":"Bauer D. & Wagner M. (2005) A canonical form for unit root processes in the state space framework. Technical report, TU Wien, Austria."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090579","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T20:32:19Z","timestamp":1554755539000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090579\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0266466608090579"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090579","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}