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In this paper a method is produced that gives an excellent approximation to the distribution function, even in the case where the process is strictly noninvertible. Also studied is the related problem of the distribution of the maximum likelihood estimator of the signalto-noise ratio in the local level model.<\/jats:p>","DOI":"10.1017\/s0266466600007726","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:46:55Z","timestamp":1236700015000},"page":"377-401","source":"Crossref","is-referenced-by-count":14,"title":["Distribution of the ML Estimator of an MA(1) and a local level model"],"prefix":"10.1017","volume":"9","author":[{"given":"Neil","family":"Shephard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600007726_ref033","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1993.10476311"},{"key":"S0266466600007726_ref022","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703732"},{"key":"S0266466600007726_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2233168"},{"volume-title":"Time Series Models","year":"1981","author":"Harvey","key":"S0266466600007726_ref017"},{"key":"S0266466600007726_ref027","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1960.10482064"},{"key":"S0266466600007726_ref016","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316429"},{"key":"S0266466600007726_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/2346911"},{"key":"S0266466600007726_ref010","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/60.2.415"},{"key":"S0266466600007726_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(81)90032-4"},{"key":"S0266466600007726_ref007","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.1.89"},{"key":"S0266466600007726_ref002","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1986.tb00492.x"},{"volume-title":"The Statistical Analysis of Time Series","year":"1971","author":"Anderson","key":"S0266466600007726_ref001"},{"key":"S0266466600007726_ref006","first-page":"691","article-title":"Small-sample properties of the maximum likelihood estimator in the first-order moving average model","volume":"68","author":"Cryer","year":"1981","journal-title":"Biometrika"},{"key":"S0266466600007726_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3424-6"},{"key":"S0266466600007726_ref026","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3242-6"},{"volume-title":"Proceedings of the Econometric Society Meeting 1979: Selected Econometric Papers in Memory of Stephan Valananis","year":"1979","author":"Davidson","key":"S0266466600007726_ref008"},{"key":"S0266466600007726_ref005","first-page":"625","article-title":"A note on the estimation of the parameters of the autoregressive-moving average process","volume":"64","author":"Cooper","year":"1977","journal-title":"Biometrika"},{"key":"S0266466600007726_ref031","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7821-5_14"},{"key":"S0266466600007726_ref023","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1947.tb02394.x"},{"key":"S0266466600007726_ref029","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004692"},{"key":"S0266466600007726_ref015","doi-asserted-by":"crossref","DOI":"10.1063\/1.3062237","volume-title":"Toeplitz Forms and Their Applications","author":"Grenander","year":"1958"},{"key":"S0266466600007726_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(78)90004-0"},{"key":"S0266466600007726_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/2986316"},{"key":"S0266466600007726_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(88)90046-2"},{"key":"S0266466600007726_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(80)90013-5"},{"key":"S0266466600007726_ref024","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/j.2517-6161.1970.tb00830.x","article-title":"Applications of likelihood methods to models involving large numbers of parameters","volume":"32","author":"Kalbfleisch","year":"1970","journal-title":"Journal of the Royal Statistical Society, Series B"},{"volume-title":"Forecasting, Structural Time Series Models and the Kalman Filter","author":"Harvey","key":"S0266466600007726_ref020","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107049994"},{"key":"S0266466600007726_ref032","doi-asserted-by":"publisher","DOI":"10.2307\/1912159"},{"key":"S0266466600007726_ref035","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001255X"},{"key":"S0266466600007726_ref036","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-9365-9"},{"key":"S0266466600007726_ref037","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706450"},{"key":"S0266466600007726_ref014","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/69.1.29"},{"key":"S0266466600007726_ref030","doi-asserted-by":"publisher","DOI":"10.2307\/2988267"},{"key":"S0266466600007726_ref021","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/61.2.383"},{"key":"S0266466600007726_ref025","unstructured":"25. 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