{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T16:45:07Z","timestamp":1696178707770},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2008,7,9]],"date-time":"2008-07-09T00:00:00Z","timestamp":1215561600000},"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":[[2008,10]]},"abstract":"<jats:p>We consider the Breitung (2002, <jats:italic>Journal of Econometrics<\/jats:italic> 108, 343\u2013363) statistic \u03be<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, which provides a nonparametric test of the I(1) hypothesis. If \u03be denotes the limit in distribution of \u03be<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> as <jats:italic>n<\/jats:italic> \u2192 \u221e, we prove (Theorem 1) that 0 \u2264 \u03be \u2264 1\/\u03c0<jats:sup>2<\/jats:sup>, a result that holds under any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called cotangent method associated with Cauchy's residue theorem.<\/jats:p>","DOI":"10.1017\/s0266466608080675","type":"journal-article","created":{"date-parts":[[2008,7,9]],"date-time":"2008-07-09T08:43:45Z","timestamp":1215593025000},"page":"1443-1455","source":"Crossref","is-referenced-by-count":1,"title":["NOTES AND PROBLEMS A GENERAL BOUND FOR THE LIMITING DISTRIBUTION OF BREITUNG'S STATISTIC"],"prefix":"10.1017","volume":"24","author":[{"given":"James","family":"Davidson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan R.","family":"Magnus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Wiegerinck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,7,9]]},"reference":[{"key":"S0266466608080675_ref010","volume-title":"Time Series Analysis: Nonstationary and Noninvertible Distribution Theory","author":"Tanaka","year":"1996"},{"key":"S0266466608080675_ref009","first-page":"229","article-title":"Some continuant determinants arising in physics and chemistry","volume":"62","author":"Rutherford","year":"1946","journal-title":"Proceedings of the Royal Society of Edinburgh, Section A"},{"key":"S0266466608080675_ref005","first-page":"427","article-title":"Distribution of the estimates for autoregressive time series with a unit root","volume":"74","author":"Dickey","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466608080675_ref004","volume-title":"The Methodology and Practice of Econometrics","author":"Davidson","year":"2008"},{"key":"S0266466608080675_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810800"},{"key":"S0266466608080675_ref008","doi-asserted-by":"crossref","DOI":"10.2307\/2531754","volume-title":"Matrix Differential Calculus with Applications in Statistics and Econometrics","author":"Magnus","year":"1988"},{"key":"S0266466608080675_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00139-7"},{"key":"S0266466608080675_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00197-5"},{"key":"S0266466608080675_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90104-Y"},{"key":"S0266466608080675_ref003","doi-asserted-by":"crossref","unstructured":"Conway J.B. (1978) Functions of One Complex Variable I, 2nd ed., Graduate Texts in Mathematics. Springer-Verlag.","DOI":"10.1007\/978-1-4612-6313-5"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608080675","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T22:23:46Z","timestamp":1556663026000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608080675\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,9]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,10]]}},"alternative-id":["S0266466608080675"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608080675","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7,9]]}}}