{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T20:56:11Z","timestamp":1777409771899,"version":"3.51.4"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":6805,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:p>For a general stationary ARMA(<jats:italic>p,q<\/jats:italic>) process <jats:italic>u<\/jats:italic> we derive the <jats:italic>exact<\/jats:italic> form of the orthogonalizing matrix <jats:italic>R<\/jats:italic> such that <jats:italic>R<\/jats:italic>\u2032<jats:italic>R<\/jats:italic> = \u03a3<jats:sup>\u22121<\/jats:sup>, where \u03a3 = <jats:italic>E<\/jats:italic>(<jats:italic>uu<\/jats:italic>\u2032) is the covariance matrix of <jats:italic>u<\/jats:italic>, generalizing the known formulae for <jats:italic>AR<\/jats:italic>(<jats:italic>p<\/jats:italic>) processes. In a linear regression model with an ARMA(<jats:italic>p,q<\/jats:italic>) error process, transforming the data by <jats:italic>R<\/jats:italic> yields a regression model with white-noise errors. We also consider an application to semi-recursive (being recursive for the model parameters, but not for the parameters of the error process) estimation.<\/jats:p>","DOI":"10.1017\/s0266466600010756","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:11:56Z","timestamp":1287393116000},"page":"95-111","source":"Crossref","is-referenced-by-count":16,"title":["The GLS Transformation Matrix and a Semi-recursive Estimator for the Linear Regression Model with ARMA Errors"],"prefix":"10.1017","volume":"8","author":[{"given":"John W.","family":"Galbraith","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victoria","family":"Zinde-Walsh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600010756_manual_ref-1","volume-title":"Advanced Econometrics","author":"Amemiya","year":"1985"},{"key":"S0266466600010756_manual_ref-7","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1093\/biomet\/71.2.273","article-title":"A method for autoregressive-moving average estimation","volume":"72","author":"Hannan","year":"1984","journal-title":"Biometrika"},{"key":"S0266466600010756_manual_ref-12","first-page":"49\u201358","article-title":"Maximum likelihood estimation of regression models with autoregressive-moving average disturbances","volume":"66","author":"Harvey","year":"1979","journal-title":"Biometrika"},{"key":"S0266466600010756_manual_ref-14","volume-title":"The Impact of Structural Breaks on Unit-Root Tests","author":"Hendry","year":"1989"},{"key":"S0266466600010756_manual_ref-2","volume-title":"Time Series Analysis Forecasting and Control","author":"Box","year":"1970"},{"key":"S0266466600010756_manual_ref-9","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1080\/01621459.1988.10478622","article-title":"Regression procedures for ARMA estimation","volume":"83","author":"Hannan","year":"1988","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600010756_manual_ref-15","volume-title":"The Theory and Practice of Econometrics","author":"Judge","year":"1985"},{"key":"S0266466600010756_manual_ref-19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511599293","volume-title":"Statistical Foundations of Econometric Modelling","author":"Spanos","year":"1986"},{"key":"S0266466600010756_manual_ref-20","doi-asserted-by":"crossref","first-page":"384\u2013402","DOI":"10.1017\/S0266466600013360","article-title":"Some exact formulae for autoregressive-moving average processes","volume":"4","author":"Zinde-Walsh","year":"1988","journal-title":"Econometric Theory"},{"key":"S0266466600010756_manual_ref-10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1093\/biomet\/69.1.81","article-title":"Recursive estimation of mixed autoregressive-moving average order","volume":"69","author":"Hannan","year":"1982","journal-title":"Biometrika"},{"key":"S0266466600010756_manual_ref-13","volume-title":"PC-GIVE: An Interactive Econometric Modelling System","author":"Hendry","year":"1989"},{"key":"S0266466600010756_manual_ref-17","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(89)90087-0"},{"key":"S0266466600010756_manual_ref-5","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/72.3.573"},{"key":"S0266466600010756_manual_ref-16","volume-title":"Theory and Practice of Recursive Identification. 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