{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T22:21:59Z","timestamp":1767046919120},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2001,7,27]],"date-time":"2001-07-27T00:00:00Z","timestamp":996192000000},"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":[[2001,8]]},"abstract":"<jats:p>Hylleberg, Engle, Granger, and Yoo (1990, <jats:italic>Journal \nof Econometrics<\/jats:italic> 44, 215\u2013238), Beaulieu and Miron \n(1993, <jats:italic>Journal of Econometrics<\/jats:italic> 55, 305\u2013328), \nGhysels, Lee, and Noh (1994, <jats:italic>Journal of Econometrics<\/jats:italic> \n62, 415\u2013442), Smith and Taylor (1998, <jats:italic>Journal \nof Econometrics<\/jats:italic> 85, 269\u2013288; 1999, <jats:italic>Journal \nof Time Series Analysis<\/jats:italic> 20, 453\u2013476; 1999, Discussion \npaper 99-15 in economics, University of Birmingham), and \nTaylor (1998, <jats:italic>Journal of Time Series Analysis<\/jats:italic> \n19, 349\u2013368) have developed a method of testing for \nseasonal unit roots of zero and nonzero frequencies. They \npropose to use <jats:italic>t<\/jats:italic>- and <jats:italic>F<\/jats:italic>-statistics as \ncriteria that are obtained from an auxiliary regression \nand find their limiting distributions as the number of \nobservations becomes large. Their limiting distributions \nare expressed by means of Brownian motions. In this paper \nthe moment generating functions associated with the limiting \ndistributions are derived, and it is shown, as in Nabeya \n(2000, <jats:italic>Econometric Theory<\/jats:italic> 16, 200\u2013230), \nthat the limiting distribution of <jats:italic>t<\/jats:italic> is well approximated \nby a distribution given in Gram\u2013Charlier series. \nThe limiting distribution of <jats:italic>F<\/jats:italic> is also well approximated \nby another type of distribution.<\/jats:p>","DOI":"10.1017\/s0266466601174037","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:16:52Z","timestamp":1027775812000},"page":"711-737","source":"Crossref","is-referenced-by-count":7,"title":["APPROXIMATION TO THE LIMITING DISTRIBUTION OF <i>t-<\/i> \nAND <i>F-<\/i>STATISTICS IN TESTING FOR SEASONAL UNIT \nROOTS"],"prefix":"10.1017","volume":"17","author":[{"given":"Seiji","family":"Nabeya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2001,7,27]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466601174037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T19:21:14Z","timestamp":1554751274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466601174037\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,7,27]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2001,8]]}},"alternative-id":["S0266466601174037"],"URL":"https:\/\/doi.org\/10.1017\/s0266466601174037","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,7,27]]}}}