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The method is based on combining the Cholesky decomposition method for complete data VARMA evaluation and the Sherman-Morrison-Woodbury formula. Potential saving for pure VAR processes is discussed and formulae for the estimation of missing values and shocks are provided. A theorem on the determinant of a low rank update is proved. Matlab implementation of the algorithm is in a companion article.<\/jats:p>","DOI":"10.1145\/1377603.1377608","type":"journal-article","created":{"date-parts":[[2008,7,29]],"date-time":"2008-07-29T13:22:19Z","timestamp":1217337739000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Evaluating exact VARMA likelihood and its gradient when data are incomplete"],"prefix":"10.1145","volume":"35","author":[{"given":"Kristjan","family":"Jonasson","sequence":"first","affiliation":[{"name":"University of Iceland, Reykjavik, Iceland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian E.","family":"Ferrando","sequence":"additional","affiliation":[{"name":"Ryerson University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,7,25]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/66.1.59"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.1.275"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/17326"},{"volume-title":"Matrix Computations","author":"Golub G. 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South African Statistical J. 15, 2, 137--193.","journal-title":"South African Statistical J."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/382043.382304"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/84.4.919"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.3.511"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/382043.382316"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.2307\/2347692"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729893"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706636"},{"volume-title":"Inverting modified matrices. Memor. rep. 42","author":"Woodbury M. A.","key":"e_1_2_1_24_1","unstructured":"Woodbury , M. A. 1950. Inverting modified matrices. Memor. rep. 42 , Statistical Research Group , Princeton University , Princeton, NJ. Woodbury, M. A. 1950. 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