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For regression models alternative asymptotically equivalent misspecification tests may lead to conflicting inference in small samples. Effective misspecification tests should have correct significance levels irrespective of the true parameters and any redundant regressors in the model, and reasonable power against a wide class of alternative specifications. A simulation study of various tests for serial correlation and predictive failure in models with lagged dependent variables finds many tests defective in small samples. Only particular degrees of freedom adjustments to the test statistics yield improved small sample behaviour.
Jan F. Kiviet (Tue,) studied this question.