Contribution to the statistical inference of vector autoregressive and error correction models.

Summary In this thesis we extend the scope of vector autoregressive models (VAR) by considering uncorrelated but dependent errors. More precisely, by studying estimation problems and the behavior of statistical tools, we are interested in the validity in our framework of results valid under the assumption of iid Gaussian iinovations. We show that the asymptotic behavior of the estimators of short term parameters and residual autocorrelations is different from the standard case. Thus, modified portmanteau tests whose asymptotic distribution is a weighted sum of chi-squares are proposed. We present an algorithm to implement these tests. The behavior of the estimators of the long-run parameters and of the likelihood ratio test for the cointegration rank is studied. It is shown that the standard results for long-run relationships extend to our framework. We also show that the asymptotic behavior of the estimators of the adjustment parameters is different from the Gaussian iid case. Theoretical examples that justify our approach are shown. The finite distance behavior of different tests is studied by Monte Carlo experiments.