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In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.
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Commentaire de M. Timothy Mark Executive Director / Directeur général Canadian Association of Research Libraries / Association des bibliothèques de recherche du Canada. Room / Pièce 239. 65 University Private / 65 université privé. Ottawa ON K1N 9A5 Tel / tél : 613.562.5385 Fax / téléc : 613.562.5195 www.carl-abrc.ca «J'ai lu avec beaucoup d'intêret et d'enthousiasme l'article Statistiques 2004-2005 et 2005 des bibliothèques universitaires et de recherche au Canada qui vient de paraître dans la revue Documentation et bibliothèques. Permettez-moi de vous féliciter, madame, sur un article qui démontre un haut niveau de recherche et d'analyse. A titre d'intérêt, l'article sera mentionné dans notre publication hebdomadaire "Cyberavis" demain. ( Prière de consulter le site web de l'ABRC). Recevez, madame, mes salutations less meilleures. Tim Mark. (Courriel daté du 14 février 2008) ==========================================