A1282
Title: The joint asymptotic distribution of permutation entropy and complexity
Authors: Angelika Silbernagel - Helmut Schmidt University (Germany) [presenting]
Christian Weiss - Helmut Schmidt University (Germany)
Abstract: Since they were first introduced, ordinal patterns have gained popularity as a method for data analysis. As the term suggests, ordinal patterns capture the ordinal structure of the underlying data. They have many desirable properties, like invariance under monotone transformations, robustness with respect to small noise, and extremely fast calculation. Later, the permutation entropy-complexity pair, which is based on ordinal patterns, emerged as a popular tool for summarizing the time-series dynamics. To best of knowledge, one of the main gaps of this tool so far is the lack of a theoretical foundation for its estimation uncertainty. Although deriving the exact (joint) sampling distribution of entropy and complexity is hardly possible, a promising approach is to make use of its asymptotic properties. Therefore, the asymptotic distribution of the entropy-complexity pair is deduced under mild dependence conditions, making the necessary distinction between a uniform and a non-uniform ordinal pattern distribution. In that way, two different limit theorems are obtained. Finally, the theory is complemented by proposing methods for visualizing the estimation uncertainty.
