Ordinal Patterns

Ordinal patterns are a useful tool in time series analysis that convert short segments of data into permutations describing their relative order. This transformation makes it easier to study complex dynamics because ordinal patterns are unaffected by strictly monotonic transformations and are robust to outliers.

Ordinal patterns are well suited for distribution-free tests. In statistical process control (SPC), they can also be used to build nonparametric control charts that monitor processes without requiring specific distributional assumptions.

StatsOrdinalPatterns.jl provides functions for computing ordinal patterns from time series data and for conducting tests based on these patterns. It also enables the replication of several studies listed below.

References

Bandt, Christoph, and Bernd Pompe. 2002. “Permutation Entropy: A Natural Complexity Measure for Time Series.” Physical Review Letters 88 (17). https://doi.org/10.1103/physrevlett.88.174102.

Bandt, Chstoph, and Faten Shiha. 2007. “Order Patterns in Time Series.” Journal of Time Series Analysis 28 (5): 646–65.

Keller, Karsten, Mathieu Sinn, and Jan Emonds. 2007. “Time Series from the Ordinal Viewpoint.” Stochastics and Dynamics 7 (02): 247–72.

Schnurr, Alexander, and Herold Dehling. 2017. “Testing for Structural Breaks via Ordinal Pattern Dependence.” Journal of the American Statistical Association 112 (518): 706–20. https://doi.org/10.1080/01621459.2016.1164706.

Weiß, Christian H. 2021. “Measuring Dispersion and Serial Dependence in Ordinal Time Series Based on the Cumulative Paired \(\phi\)-Entropy.” Entropy 24 (1): 42. https://www.mdpi.com/1099-4300/24/1/42.

Weiß, Christian H. 2022. “Non-Parametric Tests for Serial Dependence in Time Series Based on Asymptotic Implementations of Ordinal-Pattern Statistics.” Chaos: An Interdisciplinary Journal of Nonlinear Science 32 (9). https://pubs.aip.org/aip/cha/article-abstract/32/9/093107/2835852/Non-parametric-tests-for-serial-dependence-in-time?redirectedFrom=fulltext.

Weiß, Christian H, and Murat Caner Testik. 2023. “Nonparametric Control Charts for Monitoring Serial Dependence Based on Ordinal Patterns.” Technometrics 65 (3): 340–50.