{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T21:27:41Z","timestamp":1782422861965,"version":"3.54.5"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2001,9,25]],"date-time":"2001-09-25T00:00:00Z","timestamp":1001376000000},"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":[[2001,10]]},"abstract":"<jats:p>In this paper the asymptotic properties of ARMA processes with \ncomplex-conjugate unit roots in the AR lag polynomial are studied. \nThese processes behave quite differently from regular unit root \nprocesses (with a single root equal to one). In particular, \nthe asymptotic properties of a standardized version of the \n<jats:italic>periodogram<\/jats:italic> for such processes are analyzed, and a \nnonparametric test of the complex unit root hypothesis against \nthe stationarity hypothesis is derived. This test is applied \nto the annual change of the monthly number of unemployed in \nthe United States to see whether this time series has complex \nunit roots in the business cycle frequencies.<\/jats:p>","DOI":"10.1017\/s0266466601175055","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:16:52Z","timestamp":1027775812000},"page":"962-983","source":"Crossref","is-referenced-by-count":55,"title":["COMPLEX UNIT ROOTS AND BUSINESS CYCLES: ARE THEY REAL?"],"prefix":"10.1017","volume":"17","author":[{"given":"Herman J.","family":"Bierens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2001,9,25]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466601175055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T22:49:08Z","timestamp":1557269348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466601175055\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,9,25]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2001,10]]}},"alternative-id":["S0266466601175055"],"URL":"https:\/\/doi.org\/10.1017\/s0266466601175055","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,9,25]]}}}