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Surrogate Data Preserving All the Properties of Ordinal Patterns up to a Certain Length
Yoshito Hirata1,2, Masanori Shiro3, José M Amigó4
1Mathematics and Informatics Center, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Abstract:
We propose a method for generating surrogate data that preserves all the properties of ordinal patterns up to a certain length, such as the numbers of allowed/forbidden ordinal patterns and transition likelihoods from ordinal patterns into others. The null hypothesis is that the details of the underlying dynamics do not matter beyond the refinements of ordinal patterns finer than a predefined length. The proposed surrogate data help construct a test of determinism that is free from the common linearity assumption for a null-hypothesis.
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