Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 237, Issue 22, Pages 2893-2899Publisher
ELSEVIER
DOI: 10.1016/j.physd.2008.05.003
Keywords
Ordinal patterns; Topological permutation entropy; Time series analysis
Categories
Funding
- Spanish Ministry of Education and Science [MTM2005-04948]
- European FEDER
Ask authors/readers for more resources
Forbidden ordinal patterns are ordinal patterns (or rank blocks) that cannot appear in the orbits generated by a map taking values oil a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L-0, it has forbidden patterns of any length L >= L-0 and their number grows superexponentially with L. Using recent results on topological permutation entropy, in this paper we study the existence and some basic properties of forbidden ordinal patterns for self-maps on n-dimensional intervals. Our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns, although we conjecture that this is also the case under more general conditions. The theoretical results are nicely illustrated for n = 2 both using the naive counting estimator for forbidden patterns and Chao's estimator for the number of classes in a population. The robustness of forbidden ordinal patterns against observational white noise is also illustrated. (C) 2008 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available