This paper studies specification testing in dynamic linear models in the presence of omitted variables. The null hypothesis of interest is weak exogeneity: shocks have zero conditional expectation given their own past and the past of omitted variables. Existing tests based on quadratic forms of serial cross-correlations suffer from size distortions because their variance incorporates symmetric dependence in both directions, including causality from past shocks to present omitted variables (inverse causality). This paper proposes an asymmetric Portmanteau test that isolates violations of weak exogeneity from inverse causality, is asymptotically normal under the null, and does not require a parametric specification of the joint dynamics. An empirical application examines the Economic Policy Uncertainty shock series and rejects its weak exogeneity. Addressing this failure by controlling for omitted variables changes the estimated inflation response from negative to positive, suggesting a supply-side shock interpretation.