{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T12:50:11Z","timestamp":1762865411257},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,4,4]],"date-time":"2008-04-04T00:00:00Z","timestamp":1207267200000},"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":[[2008,8]]},"abstract":"<jats:p>This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990,<jats:italic>Journal of Econometrics<\/jats:italic>44, 215\u2013238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root<jats:italic>t<\/jats:italic>-statistic is shown to converge to the Dickey\u2013Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY<jats:italic>t<\/jats:italic>-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey\u2013Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.<\/jats:p>","DOI":"10.1017\/s0266466608080420","type":"journal-article","created":{"date-parts":[[2008,4,4]],"date-time":"2008-04-04T09:30:59Z","timestamp":1207301459000},"page":"1093-1129","source":"Crossref","is-referenced-by-count":6,"title":["TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES"],"prefix":"10.1017","volume":"24","author":[{"given":"Tomas del Barrio","family":"Castro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denise 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