Statistical Properties of the Entropy from Ordinal Patterns. (arXiv:2209.07650v1 [cs.IT])

The ultimate purpose of the statistical analysis of ordinal patterns is to
characterize the distribution of the features they induce. In particular,
knowing the joint distribution of the pair Entropy-Statistical Complexity for a
large class of time series models would allow statistical tests that are
unavailable to date. Working in this direction, we characterize the asymptotic
distribution of the empirical Shannon's Entropy for any model under which the
true normalized Entropy is neither zero nor one. We obtain the asymptotic …

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