{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T15:23:29Z","timestamp":1698765809084},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5186,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:p>This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the continuous record asymptotic results of S\u00f8rensen [29]. We also show how the stochastic integral representations can be utilized as the basis for finding the corresponding characteristic functions via the Fredholm approach of Nabeya and Tanaka [16,17], This \u201clink\u201d between those two approaches may be of general interest. We further tabulate the asymptotic distribution by inverting the characteristic function. Using the same methods, we also find the characteristic function for the asymptotic distribution for the Schmidt-Phillips [26] unit root test. Our results show very clearly the dependence of the various tests on the initial value of the time series.<\/jats:p>","DOI":"10.1017\/s0266466600008938","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:41:18Z","timestamp":1236685278000},"page":"937-966","source":"Crossref","is-referenced-by-count":15,"title":["Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend"],"prefix":"10.1017","volume":"10","author":[{"given":"Seiji","family":"Nabeya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bent E.","family":"S\u00f8rensen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008938_ref031","doi-asserted-by":"publisher","DOI":"10.2307\/1913104"},{"key":"S0266466600008938_ref029","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600010732"},{"key":"S0266466600008938_ref026","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0084.1992.tb00002.x"},{"key":"S0266466600008938_ref024","doi-asserted-by":"publisher","DOI":"10.2307\/1911357"},{"key":"S0266466600008938_ref023","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466600008938_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600008938_ref020","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004436"},{"key":"S0266466600008938_ref017","doi-asserted-by":"publisher","DOI":"10.2307\/2938338"},{"key":"S0266466600008938_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90010-Q"},{"key":"S0266466600008938_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(94)90023-X"},{"key":"S0266466600008938_ref016","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350701"},{"key":"S0266466600008938_ref011","unstructured":"11 Haldrup N. & Hylleberg S. . Integration, Near-Integration and Deterministic Trends. Working paper, University of Aarhus, Aarhus, 1991."},{"key":"S0266466600008938_ref007","first-page":"427","article-title":"Distribution of the estimators for autoregressive time series with a unit root.","volume":"74","author":"Dickey","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600008938_ref006","volume-title":"Methods of Mathematical Physics 1","author":"Courant","year":"1953"},{"key":"S0266466600008938_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466600008938_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478674"},{"key":"S0266466600008938_ref003","unstructured":"3 Cavanagh C. The Fragility of Unit Root Tests. Mimeo, Harvard University, Cambridge, 1989."},{"key":"S0266466600008938_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2297634"},{"key":"S0266466600008938_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02619-9"},{"key":"S0266466600008938_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1910998"},{"key":"S0266466600008938_ref012","volume-title":"Integral Equations","author":"Hochstadt","year":"1973"},{"key":"S0266466600008938_ref013","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/00310157"},{"key":"S0266466600008938_ref032","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706450"},{"key":"S0266466600008938_ref014","unstructured":"14 Nabeya S. Application of the Theory of Integral Equations to the Derivation of Asymptotic Distributions in Time Series Analysis. Dissertation, Hitotsubashi University, Tokyo, 1987."},{"key":"S0266466600008938_ref010","volume-title":"Introduction to Statistical Time Series","author":"Fuller","year":"1976"},{"key":"S0266466600008938_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1911521"},{"key":"S0266466600008938_ref019","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001241X"},{"key":"S0266466600008938_ref030","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005430"},{"key":"S0266466600008938_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/2938247"},{"key":"S0266466600008938_ref002","unstructured":"2 Cavanagh C. Roots Local to Unity. Discussion paper #1259. Harvard Institute of Economic Research, Cambridge, 1986."},{"key":"S0266466600008938_ref027","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177699516"},{"key":"S0266466600008938_ref028","doi-asserted-by":"publisher","DOI":"10.2307\/2938337"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600008938","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T19:58:12Z","timestamp":1557863892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600008938\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0266466600008938"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600008938","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}