What is it about?

It is shown how ordinal patterns can be used for distribution-free hypothesis tests, where the null hypothesis of serial independence in real-valued time series is tested against (possibly non-linear) serial dependence. We provide simple closed-form expressions relying on asymptotic derivations for implementing these tests. The performance of these tests is investigated with simulations, and their usefulness is illustrated by an environmental data example.

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Why is it important?

The use of ordinal patterns leads to a distribution-free method, which is attractive for applications in practice. As simple closed-form asymptotics are derived for the considered statistics, a computationally efficient implementation of the resulting hypothesis tests is possible.


To me, this article is the starting point for several follow-up research topics, such as adaptions to statistical process monitoring (sequential testing via control charts) or adaptions to discrete-valued time series (modified ordinal patterns).

Christian Weiß
Helmut-Schmidt-Universitat Universitat der Bundeswehr Hamburg

Read the Original

This page is a summary of: Non-parametric tests for serial dependence in time series based on asymptotic implementations of ordinal-pattern statistics, Chaos An Interdisciplinary Journal of Nonlinear Science, September 2022, American Institute of Physics, DOI: 10.1063/5.0094943.
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