Distribution-free tests for serial and spatial dependence, built on ordinal patterns.
Ordinal patterns replace the values of a data set by the rank order within small windows. The resulting frequencies say a great deal about the dependence structure while staying invariant under monotone transformations and robust to outliers. This package turns that idea into fast tests and control charts for time series, count data and spatial grids.
What the package covers
Three pattern families, each with descriptive statistics, hypothesis tests and sequential monitoring.
Serial dependence in continuous time series. Seven chart statistics, asymptotic and bootstrap inference, and EWMA control charts.
Discrete and rounded data where ties occur. Cayley permutations keep the ties intact instead of breaking them artificially.
Dependence on gridded data, read off the rank order inside small neighbourhoods such as a 2×2 block.
A growing set of published studies, replicated from source and re-executed every time the site is built. Weiß (2022) and Weiß and Testik (2023) are available now.
A test in five lines
Simulate an AR(1) series and ask whether its ordinal pattern frequencies are consistent with white noise.
using StatsOrdinalPatterns, Random
Random.seed!(1)
x = zeros(500)
for t in 2:500
x[t] = 0.5 * x[t-1] + randn()
end
test_op(x; chart_choice=Persistence())OPTestResult Chart: Persistence() Statistic: 0.0663 ───────────────────────────── Asymptotic test Critical value: 0.037 p-value: 0.0005 Reject H₀: true
The result object carries the statistic, the critical value, the p-value and the decision. Swapping test_op for test_op_bootstrap replaces the asymptotic critical value by a bootstrap one and lifts the restriction to pattern lengths m = 2 and m = 3.
Installation
The package is not registered yet, so install it directly from GitHub.
using Pkg
Pkg.add(url = "https://github.com/AdaemmerP/StatsOrdinalPatterns.jl")Where to go next
Work through a tutorial, or look up a function in the reference.