{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T10:23:36Z","timestamp":1791195816901,"version":"4.1.0"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T00:00:00Z","timestamp":1375747200000},"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":[[2013,12]]},"abstract":"<jats:p>We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.<\/jats:p>","DOI":"10.1017\/s0266466613000054","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T09:53:40Z","timestamp":1375782820000},"page":"1238-1288","source":"Crossref","is-referenced-by-count":26,"title":["TESTING AND INFERENCE IN NONLINEAR COINTEGRATING VECTOR ERROR CORRECTION MODELS"],"prefix":"10.1017","volume":"29","author":[{"given":"Dennis","family":"Kristensen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anders","family":"Rahbek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,8,6]]},"reference":[{"key":"S0266466613000054_ref7","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.jeconom.2010.03.003","article-title":"Testing for cointegration in vector autoregressions with non-stationary volatility","volume":"158","author":"Cavaliere","year":"2010a","journal-title":"Journal of Econometrics"},{"key":"S0266466613000054_ref34","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.jeconom.2010.03.010","article-title":"Likelihood-based inference for cointegration with nonlinear error-correction","volume":"158","author":"Kristensen","year":"2010","journal-title":"Journal of Econometrics"},{"key":"S0266466613000054_ref11","first-page":"33","article-title":"Hypothesis testing when a nuisance parameter is present only under the alternative","volume":"74","author":"Davies","year":"1987","journal-title":"Biometrika"},{"key":"S0266466613000054_ref38","volume-title":"Matrix Differential Calculus with Applications in Statistics and Econometrics","author":"Magnus","year":"1988"},{"key":"S0266466613000054_ref27","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.jeconom.2010.01.007","article-title":"Some identification problems in the cointegrated vector autoregressive model","volume":"158","author":"Johansen","year":"2010","journal-title":"Journal of Econometrics"},{"key":"S0266466613000054_ref46","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5254-2","volume-title":"Convergence of Stochastic Processes","author":"Pollard","year":"1984"},{"key":"S0266466613000054_ref13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0304-4076(02)00093-3","article-title":"Nonlinear minimization estimators in the presence of cointegrating relations","volume":"110","author":"de Jong","year":"2002","journal-title":"Journal of Econometrics"},{"key":"S0266466613000054_ref30","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1214\/009053606000001181","article-title":"Nonparametric estimation in a nonlinear cointegration type model","volume":"35","author":"Karlsen","year":"2007","journal-title":"Annals of Statistics"},{"key":"S0266466613000054_ref50","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.jeconom.2005.06.018","article-title":"Bootstrap testing for the null of no cointegration in a threshold vector error correction model","volume":"134","author":"Seo","year":"2006","journal-title":"Journal of Econometrics"},{"key":"S0266466613000054_ref42","first-page":"2111","volume-title":"Handbook of Econometrics","volume":"4","author":"Newey","year":"1994"},{"key":"S0266466613000054_ref17","unstructured":"Gao, J. & Phillips, P.C.B. 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