White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane.

Chagas, Eduarda T. C.; Queiroz‐Oliveira, Marcelo; Rosso, Osvaldo A.; Ramos, Heitor S.; Freitas, Cristopher G. S.; Frery, Alejandro C.

Summary: This article serves two purposes. Firstly, it surveys the Bandt and Pompe methodology for the statistical community, stressing topics that are open for research. Secondly, it contributes towards a better understanding of the statistical properties of that approach for time series analysis. The Bandt and Pompe methodology consists of computing information theory descriptors from the histogram of ordinal patterns. Such descriptors lie in a 2D manifold: the entropy–complexity plane. This article provides the first proposal of a test in the entropy–complexity plane for the white noise hypothesis. Our test is based on true white noise sequences obtained from physical devices. The proposed methodology provides consistent results: It assesses sequences of true random samples as random (adequate test size), rejects correlated and contaminated sequences (sound test power) and captures the randomness of generators previously analysed in the literature.

TIME series analysis; WHITE noise; INFORMATION theory; RANDOM number generators; STATISTICAL sampling

International Statistical Review, 2022, Vol 90, Issue 2, p374

0306-7734

Academic Journal

10.1111/insr.12487