eprintid: 19391 rev_number: 9 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/01/93/91 datestamp: 2016-04-22 14:51:27 lastmod: 2021-04-02 15:51:05 status_changed: 2016-04-22 14:51:27 type: article metadata_visibility: show creators_name: Gregoir, Stéphane creators_idrefppn: 137776691 title: Efficient tests for the presence of a couple of complex conjugate unit roots in real time series ispublished: pub subjects: subjects_ECO abstract: We introduce a framework which allows us to draw a clear parallel between the test for the presence of seasonal unit roots and that for unit root at frequency 0 (or ππ). It relies on the properties of the complex conjugate integrated of order one processes which are implicitly at work in the real time series. In the same framework as that of Phillips and Perron (Biometrica 75 (1988) 335), we derive tests for the presence of a pair of conjugate complex unit roots. The asymptotic distribution we obtain are formally close to those derived by these authors but expressed with complex Wiener processes. We then introduce sequences of near-integrated processes which allow us to study the local-to-unity asymptotic of the above test statistics. We state a result on the weak convergence of the partial sum of complex near-random walks which leads to complex Orstein–Uhlenbeck processes. Drawing on Elliott et al. (Econometrica 64 (1996) 813) we then study the design of point-optimal invariant test procedures and compute their envelope employing local-to-unity asymptotic approximations. This leads us to introduce new feasible and near efficient seasonal unit root tests. Their finite sample properties are investigated and compared with the different test procedures already available (J. Econometrics 44 (1991) 215; 62 (1994) 415; 85 (1998) 269) and those introduced in the first part of the paper. date: 2006-01 date_type: published publisher: Elsevier id_number: 10.1016/j.jeconom.2004.08.019 official_url: http://tse-fr.eu/pub/30092 faculty: tse divisions: tse language: en has_fulltext: FALSE subjectsJEL: JEL_C12 subjectsJEL: JEL_C22 view_date_year: 2006 full_text_status: none publication: Journal of Econometrics volume: 130 number: 1 pagerange: 45-100 refereed: TRUE issn: 1872-6895 oai_identifier: oai:tse-fr.eu:30092 harvester_local_overwrite: oai_set harvester_local_overwrite: issn harvester_local_overwrite: faculty harvester_local_overwrite: publisher harvester_local_overwrite: id_number harvester_local_overwrite: creators_idrefppn oai_lastmod: 2016-01-20T16:19:55Z oai_set: tse oai_set: ut1c site: ut1 citation: Gregoir, Stéphane (2006) Efficient tests for the presence of a couple of complex conjugate unit roots in real time series. Journal of Econometrics, 130 (1). pp. 45-100.