{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T13:22:57Z","timestamp":1770988977535,"version":"3.50.1"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2011,11,25]],"date-time":"2011-11-25T00:00:00Z","timestamp":1322179200000},"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":[[2012,6]]},"abstract":"<jats:p>An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite-sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.<\/jats:p>","DOI":"10.1017\/s0266466611000648","type":"journal-article","created":{"date-parts":[[2011,11,25]],"date-time":"2011-11-25T10:45:22Z","timestamp":1322217922000},"page":"509-547","source":"Crossref","is-referenced-by-count":21,"title":["NONLINEAR COINTEGRATING REGRESSION UNDER WEAK IDENTIFICATION"],"prefix":"10.1017","volume":"28","author":[{"given":"Xiaoxia","family":"Shi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter C.B.","family":"Phillips","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,11,25]]},"reference":[{"key":"S0266466611000648_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176990334"},{"key":"S0266466611000648_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00132-5"},{"key":"S0266466611000648_ref12","unstructured":"Jeganathan P. (2008) Limit Theorems for Functionals of Sums That Converge to Fractional Brownian and Stable Motions. Cowles Foundation Discussion paper 1649, Yale University."},{"key":"S0266466611000648_ref2","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466611000648_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080365"},{"key":"S0266466611000648_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600010306"},{"key":"S0266466611000648_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347498"},{"key":"S0266466611000648_ref22","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00151"},{"key":"S0266466611000648_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466699153015"},{"key":"S0266466611000648_ref4","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2011.520567"},{"key":"S0266466611000648_ref1","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3982\/ECTA7502","article-title":"Inference for parameters defined by moment inequalities using generalized moment selection","volume":"78","author":"Andrews","year":"2010","journal-title":"Econometrica"},{"key":"S0266466611000648_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2005.05.008"},{"key":"S0266466611000648_ref6","unstructured":"Cheng X. (2010) Essays on weak identification and cointegrating rank selection. Ph.D. Dissertation, Yale University."},{"key":"S0266466611000648_ref7","unstructured":"de Jong R. (2002) Nonlinear Estimators with Integrated Regressors but without Exogeneity. Working paper, Michigan State University."},{"key":"S0266466611000648_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600006629"},{"key":"S0266466611000648_ref13","volume-title":"Foundations of Modern Probability","author":"Kallenberg","year":"2001"},{"key":"S0266466611000648_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.03.002"},{"key":"S0266466611000648_ref18","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00180"},{"key":"S0266466611000648_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012408"},{"key":"S0266466611000648_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990296"},{"key":"S0266466611000648_ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090269"},{"key":"S0266466611000648_ref21","doi-asserted-by":"crossref","DOI":"10.1214\/cbms\/1462061091","volume-title":"Empirical Process Theory and Applications","author":"Pollard","year":"1990"},{"key":"S0266466611000648_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2545-2"},{"key":"S0266466611000648_ref5","unstructured":"Cheng X. (2008) Robust Confidence Intervals in Nonlinear Regression under Weak Identification. Manuscript, Department of Economics, Yale University."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466611000648","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T23:49:47Z","timestamp":1639784987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466611000648\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,25]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["S0266466611000648"],"URL":"https:\/\/doi.org\/10.1017\/s0266466611000648","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11,25]]}}}