We consider the task of distinguishing between two different alternative models that can explain observed time-series data roughly equally, mainly focusing on the period-ambiguity case (aliasing). We propose a test for checking whether the rival models are observationally equivalent for now or are already distinguishable: the Vuong closeness test, which is based on the Kullback-Leibler information criterion. It is asymptotically normal and can work (in a certain sense) even in a misspecified case in which both proposed alternatives are actually wrong. This test is also very simple for practical use. We apply it to several known extrasolar planetary systems and find that our method often helps to resolve various model ambiguities emerging in astronomical practice, but prevents us from hasty conclusions in other cases.