{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T13:00:13Z","timestamp":1775653213044,"version":"3.50.1"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":6465,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite sample distribution. In general, the approximation is excellent for values of the autoregressive parameter near one. We also consider the behavior of the power function of tests based on the normalized leastsquares estimator. Interesting nonmonotonic properties are uncovered. This analysis extends the study of Perron [15] and helps to provide explanations for the finite sample results established by Nankervis and Savin [13].<\/jats:p>","DOI":"10.1017\/s0266466600004436","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:45:16Z","timestamp":1236699916000},"page":"236-252","source":"Crossref","is-referenced-by-count":14,"title":["A Continuous Time Approximation to the Stationary First-Order Autoregressive Model"],"prefix":"10.1017","volume":"7","author":[{"given":"Pierre","family":"Perron","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600004436_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(78)90025-8"},{"key":"S0266466600004436_ref020","volume-title":"Numerical Recipes: The Art of Scientific Computing","author":"Press","year":"1986"},{"key":"S0266466600004436_ref017","doi-asserted-by":"publisher","DOI":"10.2307\/1911222"},{"key":"S0266466600004436_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/2938247"},{"key":"S0266466600004436_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(88)90012-7"},{"key":"S0266466600004436_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/2938338"},{"key":"S0266466600004436_ref014","doi-asserted-by":"crossref","unstructured":"14. Nankervis J. & Savin N.E. . The exact moments of the least-squares estimator for the autoregressive model: corrections and extensions. Working Paper Series No. 86\u201323 (Department of Economics, University of Iowa, Iowa City, IA), 1988.","DOI":"10.1016\/0304-4076(88)90012-7"},{"key":"S0266466600004436_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(78)90002-7"},{"key":"S0266466600004436_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1905674"},{"key":"S0266466600004436_ref009","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730247"},{"key":"S0266466600004436_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1910998"},{"key":"S0266466600004436_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1911521"},{"key":"S0266466600004436_ref006","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466600004436_ref021","volume-title":"Statistical Inference in Dynamic Economic Models","author":"Rubin","year":"1950"},{"key":"S0266466600004436_ref001","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold","year":"1974"},{"key":"S0266466600004436_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466600004436_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1913791"},{"key":"S0266466600004436_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600004436_ref004","unstructured":"4. Cavanagh C. Roots local to unity. Mimeo, Harvard University, 1986."},{"key":"S0266466600004436_ref005","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478674"},{"key":"S0266466600004436_ref016","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001241X"},{"key":"S0266466600004436_ref003","unstructured":"3. Bobkoski M.J. Hypothesis testing in nonstationary time series. Ph.D. Thesis, University of Wisconsin, Madison, WI, 1983."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600004436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T09:50:08Z","timestamp":1684921808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600004436\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0266466600004436"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600004436","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}