{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T22:32:08Z","timestamp":1788388328978,"version":"build-2803163510"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,2]],"date-time":"2012-09-02T00:00:00Z","timestamp":1346544000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>We calculate, by simulations, numerical asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real\u2010valued parameter <jats:italic>b<\/jats:italic> which must be estimated, simple tabulation is not feasible. Partly owing to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, <jats:italic>q<\/jats:italic>, and a value of <jats:italic>b<\/jats:italic>, provides either a set of critical values or the asymptotic <jats:italic>P<\/jats:italic>\u2010value for any value of the likelihood ratio statistic. Copyright \u00a9 2012 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.2295","type":"journal-article","created":{"date-parts":[[2012,9,2]],"date-time":"2012-09-02T21:53:17Z","timestamp":1346622797000},"page":"161-171","source":"Crossref","is-referenced-by-count":47,"title":["NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS"],"prefix":"10.1002","volume":"29","author":[{"given":"James G.","family":"MacKinnon","sequence":"first","affiliation":[{"name":"Department of Economics Queen's University  Kingston Ontario Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Morten \u00d8rregaard","family":"Nielsen","sequence":"additional","affiliation":[{"name":"Department of Economics Queen's University  Kingston Ontario Canada"},{"name":"CREATES Aarhus University  Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2012,9,2]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2533961"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA9099"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2008.11.008"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00785.x"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(88)90041-3"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2938278"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080274"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.03.006"},{"key":"e_1_2_8_10_1","article-title":"Likelihood inference for a fractionally cointegrated vector autoregressive model","author":"Johansen S","year":"2012","journal-title":"Econometrica"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/169702.169698"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1255(199611)11:6<601::AID-JAE417>3.0.CO;2-T"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1255(199909\/10)14:5<563::AID-JAE530>3.0.CO;2-R"},{"key":"e_1_2_8_14_1","unstructured":"NielsenM\u00d8 MorinL.2012.FCVARmodel.m: a Matlab software package for estimation and testing in the fractionally cointegrated VAR model. 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