Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models
نویسنده
چکیده
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. The purpose of this paper is to present the likelihood methods for the analysis of cointegration in VAR models with Gaussian errors, seasonal dummies, and constant terms. We discuss likelihood ratio tests of cointegration rank and find the asymptotic distribution of the test statistics. We characterize the maximum likelihood estimator of the cointegrating relations and formulate tests of structural hypotheses about these relations. We show that the asymptotic distribution of the maximum likelihood estimator is mixed Gaussian. Once a certain eigenvalue problem is solved and the eigenvectors and eigenvalues calculated, one can conduct inference on the cointegrating rank using some nonstandard distributions, and test hypotheses about cointegrating relations using the x2 distribution.
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