{"title":"指数函数的雅可比矩阵","authors":"J. Magnus, H. Pijls, Enrique Sentana","doi":"10.2139/ssrn.3631767","DOIUrl":null,"url":null,"abstract":"Abstract We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parameterization of rotation matrices governing impulse response functions in structural vector autoregressions.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"The Jacobian of the Exponential Function\",\"authors\":\"J. Magnus, H. Pijls, Enrique Sentana\",\"doi\":\"10.2139/ssrn.3631767\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parameterization of rotation matrices governing impulse response functions in structural vector autoregressions.\",\"PeriodicalId\":299310,\"journal\":{\"name\":\"Econometrics: Mathematical Methods & Programming eJournal\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrics: Mathematical Methods & Programming eJournal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3631767\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics: Mathematical Methods & Programming eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3631767","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parameterization of rotation matrices governing impulse response functions in structural vector autoregressions.
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