  We consider the task of distinguishing between two different alternative
models that can roughly equally explain observed time series data, mainly
focusing on the period ambiguity case (aliasing). We propose a test for
checking whether the rival models are observationally equivalent for now or
they are already distinguishable. It is the Vuong closeness test, which is
based on the Kullback-Leibler Information Criterion. It is asymptotically
normal and can work (in certain sense) even in the misspecified case, when the
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 preventing us from hasty conclusions in
other cases.
