Nonparametric testing of spatial dependence in 2D and 3D random fields
Year: 2026
Type: article
Abstract: We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert curves. We then apply ordinal pattern-based tests for serial dependence to this series. Because Hilbert curves preserve spatial locality, spatial dependence in the original field manifests as serial dependence in the transformed sequence. The approach is easy to implement, accommodates arbitrary grid sizes through generalized Hilbert ("gilbert") curves, and naturally extends beyond three dimensions. This provides a practical and general alternative to existing methods based on spatial ordinal patterns, which are typically limited to two-dimensional settings.
DOI: 10.1063/5.0307955
Authors: Christian H. Weiß, Philipp Adämmer
Institutions: Helmut Schmidt University, Universität Greifswald
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: hybrid
OpenAlex ID: W4415879057