{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T14:10:03Z","timestamp":1714140603568},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2012,7,6]],"date-time":"2012-07-06T00:00:00Z","timestamp":1341532800000},"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":[[2013,4]]},"abstract":"<jats:p>Testing for the presence of a broken linear trend when the nature of the persistence in the data is unknown is not a trivial problem, because the test needs to be both asymptotically correctly sized and consistent, regardless of the order of integration of the data. In a recent paper, Sayginsoy and Vogelsang (2011,<jats:italic>Econometric Theory<\/jats:italic>27, 992\u20131025) (SV) show that tests based on fixed-<jats:italic>b<\/jats:italic>asymptotics provide a useful solution to this problem in the case where the shocks may be either weakly dependent or display strong dependence within the near-unit-root class. In this paper we analyze the performance of these tests when the shocks may be fractionally integrated, an alternative model paradigm that allows for either weak or strong dependence in the shocks. We demonstrate that the fixed-<jats:italic>b<\/jats:italic>trend break statistics converge to well-defined limit distributions under both the null and local alternatives in this case (and retain consistency against fixed alternatives), but that these distributions depend on the fractional integration parameter<jats:italic>\u03b4<\/jats:italic>. As a result, it is only when<jats:italic>\u03b4<\/jats:italic>is either zero or one that the SV critical values yield correctly sized tests. Consequently, we propose a procedure that employs<jats:italic>\u03b4<\/jats:italic>-adaptive critical values to remove the size distortions in the SV test. In addition, use of<jats:italic>\u03b4<\/jats:italic>-adaptive critical values also allows us to consider a simplification of the SV test that is (asymptotically) correctly sized across<jats:italic>\u03b4<\/jats:italic>but can also provide a significant increase in power over the standard SV test when<jats:italic>\u03b4<\/jats:italic>= 1.<\/jats:p>","DOI":"10.1017\/s0266466612000291","type":"journal-article","created":{"date-parts":[[2012,7,6]],"date-time":"2012-07-06T11:53:43Z","timestamp":1341575623000},"page":"393-418","source":"Crossref","is-referenced-by-count":6,"title":["ON THE BEHAVIOR OF FIXED-<i>b<\/i>TREND BREAK TESTS UNDER FRACTIONAL INTEGRATION"],"prefix":"10.1017","volume":"29","author":[{"given":"Fabrizio","family":"Iacone","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen J.","family":"Leybourne","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.M. Robert","family":"Taylor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,7,6]]},"reference":[{"key":"S0266466612000291_ref14","first-page":"278","volume-title":"Palgrave Handbook of Econometrics, vol. 1: Econometric Theory","author":"Perron","year":"2006"},{"key":"S0266466612000291_ref5","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1017\/S0266466609990259","article-title":"Testing for a unit root in the presence of a possible break in trend","volume":"25","author":"Harris","year":"2009","journal-title":"Econometric Theory"},{"key":"S0266466612000291_ref7","unstructured":"Iacone, F. , Leybourne, S.J. , & Taylor, A.M.R. (2011) Testing for a Break in the Trend when the Order of Integration Is Unknown. Mimeo, University of Nottingham."},{"key":"S0266466612000291_ref10","doi-asserted-by":"crossref","first-page":"2093","DOI":"10.1111\/1468-0262.00366","article-title":"Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation","volume":"70","author":"Kiefer","year":"2002","journal-title":"Econometrica"},{"key":"S0266466612000291_ref1","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.jeconom.2007.01.020","article-title":"Nonstationarity-extended local Whittle estimation","volume":"141","author":"Abadir","year":"2007","journal-title":"Journal of Econometrics"},{"key":"S0266466612000291_ref18","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1017\/S0266466610000617","article-title":"Testing for a shift in trend at an unknown date: A fixed- b analysis of heteroskedasticity autocorrelation robust OLS based tests","volume":"27","author":"Sayginsoy","year":"2011","journal-title":"Econometric Theory"},{"key":"S0266466612000291_ref16","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.jeconom.2004.09.009","article-title":"Cointegration in fractional systems with deterministic trends","volume":"129","author":"Robinson","year":"2005","journal-title":"Journal of Econometrics"},{"key":"S0266466612000291_ref2","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.2307\/2951753","article-title":"Optimal tests when a nuisance parameter is present only under the alternative","volume":"62","author":"Andrews","year":"1994","journal-title":"Econometrica"},{"key":"S0266466612000291_ref15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.jeconom.2004.09.004","article-title":"Structural breaks with deterministic and stochastic trends","volume":"129","author":"Perron","year":"2005","journal-title":"Journal of Econometrics"},{"key":"S0266466612000291_ref9","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1017\/S0266466611000697","article-title":"A necessary moment condition for the fractional functional central limit theorem","volume":"28","author":"Johansen","year":"2012","journal-title":"Econometric Theory"},{"key":"S0266466612000291_ref17","unstructured":"Sayginsoy, \u00d6. & Vogelsang, T. (2008) Testing for a Shift in Trend at an Unknown Date: A Fixed- b Analysis of Heteroskedasticity Autocorrelation Robust OLS Based Tests. Working paper, Michigan State University."},{"key":"S0266466612000291_ref21","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/07350015.1992.10509904","article-title":"Further evidence on the great crash, the oil price shock and the unit root hypothesis","volume":"10","author":"Zivot","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466612000291_ref6","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1017\/S0266466608090385","article-title":"Simple, robust and powerful tests of the breaking trend hypothesis","volume":"25","author":"Harvey","year":"2009","journal-title":"Econometric Theory"},{"key":"S0266466612000291_ref4","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316429","volume-title":"Multiple Time Series","author":"Hannan","year":"1970"},{"key":"S0266466612000291_ref11","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0378-3758(98)00245-6","article-title":"Alternative forms of fractional Brownian motion","volume":"80","author":"Marinucci","year":"1999","journal-title":"Journal of Statistical Planning and Inference"},{"key":"S0266466612000291_ref8","unstructured":"Iacone, F. , Leybourne, S.J. , & Taylor, A.M.R. (2012) On the Behaviour of Fixed- b Trend Break Tests under Fractional Integration. Granger Centre for Time Series Econometrics Working Paper series 12\/01."},{"key":"S0266466612000291_ref12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0304-4149(99)00088-5","article-title":"Weak convergence of multivariate fractional processes","volume":"86","author":"Marinucci","year":"2000","journal-title":"Stochastic Processes and Their Applications"},{"key":"S0266466612000291_ref3","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1198\/073500104000000631","article-title":"Powerful trend function tests that are robust to strong serial correlation with an application to the Prebisch-Singer hypothesis","volume":"23","author":"Bunzel","year":"2005","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466612000291_ref20","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/07350015.1998.10524736","article-title":"Testing for a shift in mean without having to estimate serial correlation parameters","volume":"16","author":"Vogelsang","year":"1998","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466612000291_ref19","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/BF02760564","article-title":"Long memory versus structural breaks: An overview","volume":"45","author":"Sibbertsen","year":"2004","journal-title":"Statistical Papers"},{"key":"S0266466612000291_ref13","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.2307\/1913712","article-title":"The great crash, the oil price shock and the unit root hypothesis","volume":"57","author":"Perron","year":"1989","journal-title":"Econometrica"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466612000291","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T13:52:51Z","timestamp":1714139571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466612000291\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,6]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,4]]}},"alternative-id":["S0266466612000291"],"URL":"https:\/\/doi.org\/10.1017\/s0266466612000291","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,6]]}}}