{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T18:42:04Z","timestamp":1785350524459,"version":"3.55.0"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T00:00:00Z","timestamp":1200960000000},"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":[[2008,6]]},"abstract":"<jats:p>An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial inconsistent stationarity tests with correct asymptotic size.<\/jats:p>","DOI":"10.1017\/s0266466608080250","type":"journal-article","created":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T10:15:58Z","timestamp":1200996958000},"page":"616-630","source":"Crossref","is-referenced-by-count":28,"title":["THE IMPOSSIBILITY OF CONSISTENT DISCRIMINATION BETWEEN I(0) AND I(1) PROCESSES"],"prefix":"10.1017","volume":"24","author":[{"given":"Ulrich K.","family":"M\u00dcller","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,1,22]]},"reference":[{"key":"S0266466608080250_ref018","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00318"},{"key":"S0266466608080250_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00139-7"},{"key":"S0266466608080250_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.08.012"},{"key":"S0266466608080250_ref016","doi-asserted-by":"publisher","DOI":"10.2307\/2171788"},{"key":"S0266466608080250_ref005","unstructured":"Davidson J. 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