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Our tests are useful for<jats:sc>Garch<\/jats:sc>models and in many empirically relevant macro and finance applications involving<jats:sc>Var<\/jats:sc>s and multivariate regressions. We determine the rank of the differences between the estimators' asymptotic covariance matrices under correct specification, and take into account that some parameters remain consistently estimated under distributional misspecification. We provide finite sample results through Monte Carlo simulations. 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