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More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some finite-sample superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation.<\/jats:p>","DOI":"10.1017\/s0266466610000629","type":"journal-article","created":{"date-parts":[[2011,3,25]],"date-time":"2011-03-25T11:33:55Z","timestamp":1301052835000},"page":"1026-1047","source":"Crossref","is-referenced-by-count":3,"title":["SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS"],"prefix":"10.1017","volume":"27","author":[{"given":"Patrick","family":"Marsh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,3,25]]},"reference":[{"key":"S0266466610000629_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(95)00061-5"},{"key":"S0266466610000629_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600007507"},{"key":"S0266466610000629_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/1426607"},{"key":"S0266466610000629_ref9","doi-asserted-by":"publisher","DOI":"10.2307\/1403269"},{"key":"S0266466610000629_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2171846"},{"key":"S0266466610000629_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466698145012"},{"key":"S0266466610000629_ref31","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466610000629_ref25","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990284"},{"key":"S0266466610000629_ref32","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/75.2.335"},{"key":"S0266466610000629_ref10","first-page":"427","article-title":"Distribution of the estimators for autoregressive series with a unit root","volume":"74","author":"Dickey","year":"1979","journal-title":"Journal of the American Statistical Society"},{"key":"S0266466610000629_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349164"},{"key":"S0266466610000629_ref4","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1214\/aos\/1030563978","article-title":"Sieve bootstrap for smoothing in nonstationary time series","volume":"26","author":"B\u00fchlmann","year":"1998","journal-title":"Annals of Statistics"},{"key":"S0266466610000629_ref5","doi-asserted-by":"publisher","DOI":"10.1198\/16214502388618636"},{"key":"S0266466610000629_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080043"},{"key":"S0266466610000629_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660809049X"},{"key":"S0266466610000629_ref19","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476825"},{"key":"S0266466610000629_ref29","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.1.91"},{"key":"S0266466610000629_ref8","doi-asserted-by":"publisher","DOI":"10.1081\/ETC-120015385"},{"key":"S0266466610000629_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90080-W"},{"key":"S0266466610000629_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.10.005"},{"key":"S0266466610000629_ref14","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1080\/00031305.1999.10474463","article-title":"Explaining the saddlepoint approximation","volume":"53","author":"Goutis","year":"1999","journal-title":"American Statistician"},{"key":"S0266466610000629_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990259"},{"key":"S0266466610000629_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325620"},{"key":"S0266466610000629_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660319202X"},{"key":"S0266466610000629_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/81.4.807"},{"key":"S0266466610000629_ref22","volume-title":"Matrix Differential Calculus, with Applications in Statistics and Econometrics","author":"Magnus","year":"1999"},{"key":"S0266466610000629_ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466607070296"},{"key":"S0266466610000629_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90010-Q"},{"key":"S0266466610000629_ref27","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00256"},{"key":"S0266466610000629_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2006.06.009"},{"key":"S0266466610000629_ref30","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466610000629_ref33","unstructured":"Richard P. 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