{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:50:44Z","timestamp":1770979844204,"version":"3.50.1"},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":7926,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1987,6]]},"abstract":"<jats:p>The distributions of the test statistics are investigated in the context of an AR(1) model where the root is unity or near unity and where the exogenous process is a stable process, a random walk or a time trend. The finite sample distributions are estimated by Monte Carlo methods assuming normal disturbances. The sensitivity of the distributions to both the values of the parameters of the AR(1) model and the process generating the exogenous time series is examined. The Monte Carlo results motivate several theorems which describe the exact sampling behavior of the test statistics. The analytical and empirical results present a mixed picture with respect to the accuracy of the relevant asymptotic approximations.<\/jats:p>","DOI":"10.1017\/s026646660001046x","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:46:34Z","timestamp":1236699994000},"page":"387-408","source":"Crossref","is-referenced-by-count":34,"title":["Finite Sample Distributions of<i>t<\/i>and<i>F<\/i>Statistics in an AR(1) Model with Anexogenous Variable"],"prefix":"10.1017","volume":"3","author":[{"given":"J.C.","family":"Nankervis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.E.","family":"Savin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S026646660001046X_ref034","unstructured":"34. West K.D. Asymptotic normality when regressors have a unit root. Princeton Discussion Paper in Economics #770, Princeton University, New Jersey, 1986."},{"key":"S026646660001046X_ref033","volume-title":"Principles of econometrics","author":"Theil","year":"1971"},{"key":"S026646660001046X_ref032","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1985.10478125"},{"key":"S026646660001046X_ref030","unstructured":"30. Phillips P.C.B. & Perron P. . Testing for a unit root in time-series regression. Cowles Foundation Discussion Paper No. 795. Yale University, Connecticut, 1986."},{"key":"S026646660001046X_ref028","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S026646660001046X_ref029","unstructured":"29. Phillips P.C.B. Towards a unified asymptotic theory for autoregression. Cowles Foundation Discussion Paper No. 795. Yale University, Connecticut, 1986."},{"key":"S026646660001046X_ref026","unstructured":"26. Park J.Y. & Phillips P.C.B. . Statistical inference in regressions with integrated processes: Part II. Cowles Foundation Discussion Paper, No. 811: Yale University, Connecticut, 1987."},{"key":"S026646660001046X_ref025","volume-title":"Nag Fortran library manual","year":"1984"},{"key":"S026646660001046X_ref024","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3932(82)90012-5"},{"key":"S026646660001046X_ref020","volume-title":"Introduction to the theory of statistics","author":"Mood","year":"1963"},{"key":"S026646660001046X_ref017","unstructured":"17. Hasza D.P. Estimation in nonstationary time series. Unpublished Ph.D. thesis. Iowa State University, 1977."},{"key":"S026646660001046X_ref016","doi-asserted-by":"publisher","DOI":"10.1086\/260724"},{"key":"S026646660001046X_ref015","unstructured":"15. Grubb D. Lag invariance in autoregressive processes. Centre for Labour Economics: London School of Economics, England, 1985."},{"key":"S026646660001046X_ref014","doi-asserted-by":"publisher","DOI":"10.1086\/261095"},{"key":"S026646660001046X_ref013","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345457"},{"key":"S026646660001046X_ref022","volume-title":"The Student's t approximation in a stationary first-order autoregressive model","author":"Nankervis","year":"1986"},{"key":"S026646660001046X_ref027","volume-title":"C.R.D.E.-Cahier 3286","author":"Perron","year":"1986"},{"key":"S026646660001046X_ref009","unstructured":"9. Domowitz I. & Muus L. . Inference in the explosive first-order linear dynamic regression model. Department of Economics: Northwestern University, Illinois, 1985."},{"key":"S026646660001046X_ref010","doi-asserted-by":"publisher","DOI":"10.1086\/261016"},{"key":"S026646660001046X_ref031","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/71.3.599"},{"key":"S026646660001046X_ref021","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(85)90084-3"},{"key":"S026646660001046X_ref005","unstructured":"5. Cavanagh C.L. & Rothenberg T.J. . Linear regression with nonnormal errors. Department of Economics: University of California at Berkeley, California, 1986."},{"key":"S026646660001046X_ref006","unstructured":"6. Dickey D.A. The estimation and hypothesis testing for nonstationary time series. Unpub lished Ph.D. thesis. Iowa State University, Iowa, 1976."},{"key":"S026646660001046X_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1909575"},{"key":"S026646660001046X_ref019","doi-asserted-by":"crossref","unstructured":"19. Malinvaud E. Private communication, 1984.","DOI":"10.1080\/07474938408800056"},{"key":"S026646660001046X_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2297634"},{"key":"S026646660001046X_ref023","volume-title":"Working paper Series No. 86\u201336","author":"Nankervis","year":"1987"},{"key":"S026646660001046X_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1912517"},{"key":"S026646660001046X_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/2553934"},{"key":"S026646660001046X_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2553149"},{"key":"S026646660001046X_ref002","volume-title":"The statistical analysis of time series","author":"Anderson","year":"1971"},{"key":"S026646660001046X_ref012","volume-title":"Introduction to statistical time series","author":"Fuller","year":"1976"},{"key":"S026646660001046X_ref004","doi-asserted-by":"publisher","DOI":"10.1145\/361604.361629"},{"key":"S026646660001046X_ref007","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1080\/00031305.1986.10475349","article-title":"Unit roots in time-series models: Tests and implications","volume":"40","author":"Dickey","year":"1986","journal-title":"American Statistician"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646660001046X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T09:28:14Z","timestamp":1710149294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646660001046X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,6]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1987,6]]}},"alternative-id":["S026646660001046X"],"URL":"https:\/\/doi.org\/10.1017\/s026646660001046x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,6]]}}}