{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T16:54:30Z","timestamp":1783356870344,"version":"3.54.6"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2012,7,30]],"date-time":"2012-07-30T00:00:00Z","timestamp":1343606400000},"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>This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root throughout the sample against the alternative hypothesis that the process alternates between stationary and unit root regimes. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. We further show that the tests are inconsistent when directed against the incorrect alternative, thereby enabling identification of the nature of persistence in the initial regime. We also propose hybrid testing procedures that allow ruling out of stable stationary processes or ones that are subject to only stationary changes under the null, thereby aiding the researcher in interpreting a rejection as emanating from a switch between a unit root and stationary regime. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006, <jats:italic>Journal of Econometrics<\/jats:italic>134, 373\u2013399) which allows imposing within- and cross-regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed procedures perform well in finite samples relative to those available in the literature.<\/jats:p>","DOI":"10.1017\/s0266466612000357","type":"journal-article","created":{"date-parts":[[2012,7,30]],"date-time":"2012-07-30T08:52:36Z","timestamp":1343638356000},"page":"289-323","source":"Crossref","is-referenced-by-count":43,"title":["WALD TESTS FOR DETECTING MULTIPLE STRUCTURAL CHANGES IN PERSISTENCE"],"prefix":"10.1017","volume":"29","author":[{"given":"Mohitosh","family":"Kejriwal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Perron","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2012,7,30]]},"reference":[{"key":"S0266466612000357_ref18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jeconom.2008.08.019","article-title":"Unit root tests allowing for a break in the trend function under both the null and alternative hypotheses","volume":"148","author":"Kim","year":"2009","journal-title":"Journal of Econometrics"},{"key":"S0266466612000357_ref20","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1017\/S0266466603194078","article-title":"Inference on segmented cointegration","volume":"19","author":"Kim","year":"2003","journal-title":"Econometric Theory"},{"key":"S0266466612000357_ref27","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1080\/01621459.1995.10476510","article-title":"Unit root tests in ARMA models with data dependent methods for the selection of the truncation lag","volume":"90","author":"Ng","year":"1995","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466612000357_ref7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jeconom.2003.10.028","article-title":"Tests of stationarity against a change in persistence","volume":"123","author":"Busetti","year":"2004","journal-title":"Journal of Econometrics"},{"key":"S0266466612000357_ref33","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1111\/j.1468-0084.2004.00117.x","article-title":"Fluctuation tests for a change in persistence","volume":"67","author":"Taylor","year":"2005","journal-title":"Oxford Bulletin of Economics and Statistics"},{"key":"S0266466612000357_ref6","doi-asserted-by":"crossref","first-page":"235","DOI":"10.2307\/2601231","article-title":"Exchange rate regimes and shifts in inflation persistence: Does nothing else matter","volume":"31","author":"Burdekin","year":"1999","journal-title":"Journal of Money, Credit and Banking"},{"key":"S0266466612000357_ref14","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.jeconom.2005.07.002","article-title":"Modified tests for a change in persistence","volume":"134","author":"Harvey","year":"2006","journal-title":"Journal of Econometrics"},{"key":"S0266466612000357_ref21","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1111\/j.1468-0084.2004.00116.x","article-title":"Detection of structural change in the long-run persistence in a univariate time series","volume":"67","author":"Kurozumi","year":"2005","journal-title":"Oxford Bulletin of Economics and Statistics"},{"key":"S0266466612000357_ref2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.2307\/2998540","article-title":"Estimating and testing linear models with multiple structural changes","volume":"66","author":"Bai","year":"1998","journal-title":"Econometrica"},{"key":"S0266466612000357_ref30","first-page":"278","volume-title":"Palgrave Handbook of Econometrics","author":"Perron","year":"2006"},{"key":"S0266466612000357_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1467-9892.1994.tb00173.x","article-title":"Recognizing overdifferenced time series","volume":"15","author":"Chang","year":"1994","journal-title":"Journal of Time Series Analysis"},{"key":"S0266466612000357_ref13","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1111\/j.1465-7295.1991.tb00837.x","article-title":"Is the budget deficit too large?","volume":"29","author":"Hakkio","year":"1991","journal-title":"Economic Inquiry"},{"key":"S0266466612000357_ref5","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1214\/aos\/1176342709","article-title":"Consistent autoregressive spectral estimates","volume":"2","author":"Berk","year":"1974","journal-title":"Annals of Statistics"},{"key":"S0266466612000357_ref17","doi-asserted-by":"crossref","unstructured":"Kejriwal, M. & Perron, P. 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