Professor Bierens' approach is definitely original and interesting. We think it might become important, in particular, for testing correct specification of models (even nonlinear) in the time series context. For example, his test in Section 6 is (to our knowledge) the first test of correct specification of a model which is consistent against all stationary alternatives. Usually, specification tests checking the structure of dependence are only designed to test against a finite-dimensional alternative. The critical points we make below should be seen in the light of our above statements.