{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T20:05:21Z","timestamp":1772481921613,"version":"3.50.1"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2005,2,8]],"date-time":"2005-02-08T00:00:00Z","timestamp":1107820800000},"content-version":"unspecified","delay-in-days":7,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2005,2]]},"abstract":"<jats:p>This paper provides a survey on a class of so-called subspace methods \nwhose main proponent is CCA proposed by Larimore (1983, <jats:italic>Proceedings of the 1983 American Control \nConference 2<\/jats:italic>). Because they are based on regressions these methods \nfor the estimation of ARMAX systems are attractive as a result of their \nconceptual simplicity and their numerical advantages as compared to \ntraditional estimators based on criterion optimization. Under the \nassumption of correct specification the methods provide consistent and \nasymptotically normal estimates for stationary ARMAX processes where \nthe innovations may be conditionally heteroskedastic and the exogenous \ninputs are strictly stationary of sufficiently short memory. For \nstationary autoregressive moving average (ARMA) processes with \nindependent and identically distributed (i.i.d.) Gaussian innovations \nthe estimates are even asymptotically efficient. For <jats:italic>I<\/jats:italic>(1) ARMA \nprocesses the estimates of both the long-run and the short-run dynamics \nare consistent without using the knowledge that the data are integrated \nin the algorithm. Additionally the algorithms provide easily accessible \ninformation on the appropriateness of the chosen model complexity. The \nalgorithms include a number of design parameters that have to be set by \nthe user. These include the order of the estimated system. This paper \ncollects up-to-date knowledge on the effects of these design \nparameters, leading to a number of suggested automated choices to \nobtain a fully automated estimation procedure.<\/jats:p>","DOI":"10.1017\/s0266466605050127","type":"journal-article","created":{"date-parts":[[2005,4,25]],"date-time":"2005-04-25T14:15:35Z","timestamp":1114438535000},"page":"181-211","source":"Crossref","is-referenced-by-count":24,"title":["ESTIMATING LINEAR DYNAMICAL SYSTEMS USING SUBSPACE METHODS"],"prefix":"10.1017","volume":"21","author":[{"given":"Dietmar","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2005,2,8]]},"reference":[{"key":"S0266466605050127_ref031","doi-asserted-by":"crossref","unstructured":"Peternell, K. , W. Scherrer , & M. Deistler (1996)Statistical analysis of novel subspace identification methods.Signal Processing 52,161\u2013177.","DOI":"10.1016\/0165-1684(96)00051-5"},{"key":"S0266466605050127_ref015","doi-asserted-by":"crossref","unstructured":"Bauer, D. & M. Wagner (2002a)Estimating cointegrated systems using subspace algorithms.Journal of Econometrics 111,47\u201384.","DOI":"10.1016\/S0304-4076(02)00119-7"},{"key":"S0266466605050127_ref022","doi-asserted-by":"crossref","unstructured":"Deistler, M. , K. Peternell , & W. Scherrer (1995)Consistency and relative efficiency of subspace methods.Automatica 31,1865\u20131875.","DOI":"10.1016\/0005-1098(95)00089-6"},{"key":"S0266466605050127_ref008","unstructured":"Bauer, D. (2004b)Estimation and Testing in Cointegrated Systems Using SubspaceMethods.Technical report,Cowles Foundation for Research in Economics, Yale University."},{"key":"S0266466605050127_ref026","doi-asserted-by":"crossref","unstructured":"Jansson, M. & B. Wahlberg (1998)On consistency of subspace methods for system identification.Automatica 34,1507\u20131519.","DOI":"10.1016\/S0005-1098(98)80004-6"},{"key":"S0266466605050127_ref014","doi-asserted-by":"crossref","unstructured":"Bauer, D. & S. de Waele (2003)A finite sample comparison of automatic model selection methods. In P. van den Hof , B. Wahlberg , & S. Weiland (eds.),Proceedings of the IFAC Symposium on System Identification,SYSID'03, Rotterdam, The Netherlands.Elsevier.","DOI":"10.1016\/S1474-6670(17)35013-9"},{"key":"S0266466605050127_ref029","doi-asserted-by":"crossref","unstructured":"Lewis, R. & G. Reinsel (1985)Prediction of multivariate time series by autoregressive modelfitting.Journal of Multivariate Analysis 16,393\u2013411.","DOI":"10.1016\/0047-259X(85)90027-2"},{"key":"S0266466605050127_ref002","doi-asserted-by":"crossref","unstructured":"Aoki, M. & A. 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