Yoshito Hirata (The University of Tokyo and University of Tsukuba), Masanori Shiro (University  National Institute of Advanced Industrial Science and Technology, Japan) and José M. Amigó (University Miguel Hernández of Elche).

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…

Keywords.  Time series analysis; determinism; Museum pass games; stochasticity; permutations; hypothesis testing.