The purpose of this paper is twofold:  On one side we aim to provide easily computable almost sure bounds for inference in presence of nuisance parameters unidentified under the null.  On the other hand, more generally, we aim to provide a flexible completely consistent procedure for inference in, possibly mispecified, parametric models, in the case of dependent and heterogeneous observationsl.  With the term completely consistent we mean that the asymptotic size is zero and the asymptotic power is one.  The small sample behavior of our procedures is analyzed via few Monte Carlo simulations, in particular we consider (i) conditional moment tests, (ii) testing for nonlinearities in the SETAR model. Overall the size approaches zerio relatively slowly, while the power approaches one very quickly.