Distinguishing between a true period and its alias, and other tasks of model discrimination

Abstract

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.