{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T14:04:48Z","timestamp":1790777088464,"version":"4.1.0"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2011,6,7]],"date-time":"2011-06-07T00:00:00Z","timestamp":1307404800000},"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":[[2011,12]]},"abstract":"<jats:p>In this paper we propose a new approximate factor model for large cross-section and time dimensions. Factor loadings are assumed to be smooth functions of time, which allows considering the model as<jats:italic>locally stationary<\/jats:italic>while permitting empirically observed time-varying second moments. Factor loadings are estimated by the eigenvectors of a nonparametrically estimated covariance matrix. As is well known in the stationary case, this principal components estimator is consistent in approximate factor models if the eigenvalues of the noise covariance matrix are bounded. To show that this carries over to our locally stationary factor model is the main objective of our paper. Under simultaneous asymptotics (cross-section and time dimension go to infinity simultaneously), we give conditions for consistency of our estimators. A simulation study illustrates the performance of these estimators.<\/jats:p>","DOI":"10.1017\/s0266466611000053","type":"journal-article","created":{"date-parts":[[2011,6,7]],"date-time":"2011-06-07T10:23:40Z","timestamp":1307442220000},"page":"1279-1319","source":"Crossref","is-referenced-by-count":51,"title":["LOCALLY STATIONARY FACTOR MODELS: IDENTIFICATION AND NONPARAMETRIC ESTIMATION"],"prefix":"10.1017","volume":"27","author":[{"given":"Giovanni","family":"Motta","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian M.","family":"Hafner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rainer","family":"von Sachs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2011,6,7]]},"reference":[{"key":"S0266466611000053_ref25","volume-title":"Handbook of Matrices","author":"L\u00fctkepohl","year":"1996"},{"key":"S0266466611000053_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aos\/1034276620","article-title":"Fitting time series models to nonstationary processes","volume":"25","author":"Dahlhaus","year":"1997","journal-title":"Annals of Statistics"},{"key":"S0266466611000053_ref24","doi-asserted-by":"publisher","DOI":"10.2307\/1924119"},{"key":"S0266466611000053_ref33","doi-asserted-by":"publisher","DOI":"10.1198\/073500102317351921"},{"key":"S0266466611000053_ref27","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00070"},{"key":"S0266466611000053_ref19","first-page":"59","volume-title":"Advances in Econometrics","volume":"20","author":"Hafner","year":"2006"},{"key":"S0266466611000053_ref32","doi-asserted-by":"publisher","DOI":"10.1198\/016214502388618960"},{"key":"S0266466611000053_ref7","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899353622"},{"key":"S0266466611000053_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1015957480"},{"key":"S0266466611000053_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/jae.3950040102"},{"key":"S0266466611000053_ref31","doi-asserted-by":"publisher","DOI":"10.1162\/0034653054638274"},{"key":"S0266466611000053_ref1","first-page":"21","volume-title":"Mastering Risk","volume":"2","author":"Alexander","year":"2001"},{"key":"S0266466611000053_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02595830"},{"key":"S0266466611000053_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00392"},{"key":"S0266466611000053_ref3","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00273"},{"key":"S0266466611000053_ref4","volume-title":"Modern Econometric Analysis","author":"Breitung","year":"2006"},{"key":"S0266466611000053_ref5","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1993.10476411"},{"key":"S0266466611000053_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/1912275"},{"key":"S0266466611000053_ref8","volume-title":"Athens Conference on Applied Probability and Time Series Analysis","volume":"II","author":"Dahlhaus","year":"1996"},{"key":"S0266466611000053_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000227"},{"key":"S0266466611000053_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90099-F"},{"key":"S0266466611000053_ref14","doi-asserted-by":"publisher","DOI":"10.1109\/78.726819"},{"key":"S0266466611000053_ref15","doi-asserted-by":"publisher","DOI":"10.1162\/003465300559037"},{"key":"S0266466611000053_ref16","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000002050"},{"key":"S0266466611000053_ref17","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1017\/S0266466601176048","article-title":"The generalized dynamic factor model: Representation theory","volume":"17","author":"Forni","year":"2001","journal-title":"Econometric Theory"},{"key":"S0266466611000053_ref18","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475090"},{"key":"S0266466611000053_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbg005"},{"key":"S0266466611000053_ref21","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1080\/10618600.1997.10474726","article-title":"Local bandwidth choice in kernel regression estimation","volume":"6","author":"Herrmann","year":"1997","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"S0266466611000053_ref23","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1993.1084"},{"key":"S0266466611000053_ref22","volume-title":"Statistics for Dependent Data, Lecture Notes in Statistics","volume":"187","author":"Herzel","year":"2006"},{"key":"S0266466611000053_ref26","doi-asserted-by":"publisher","DOI":"10.1162\/003465304323023886"},{"key":"S0266466611000053_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(76)90046-6"},{"key":"S0266466611000053_ref30","first-page":"425","article-title":"Capital asset prices: A theory of market equilibrium under conditions of risk","volume":"19","author":"Sharpe","year":"1964","journal-title":"Journal of Finance"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466611000053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T00:42:30Z","timestamp":1741221750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466611000053\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,7]]},"references-count":33,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["S0266466611000053"],"URL":"https:\/\/doi.org\/10.1017\/s0266466611000053","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,7]]}}}