WISE: A Weighted Similarity Aggregation Test for Serial Independence

2025/09/06 by Zhu, Qihua, Liu, Mingshuo, Han, Yuefeng +1
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2509.05678

Abstract

We propose a nonparametric test for serial independence that aggregates pairwise similarities of observations with lag-dependent weights. The resulting statistic is powerful to general forms of temporal dependence, including nonlinear and uncorrelated alternatives, and applies to ultra-high-dimensional and non-Euclidean data. We derive asymptotic normality under both permutation and population nulls, and establish consistency in classical large-sample and high-dimension-low-sample-size (HDLSS) regimes. The test therefore provides the first theoretical power guarantees for serial independence in the HDLSS setting. Simulations demonstrate accurate size and strong power against a wide range of alternatives, showing significant power improvement over existing methods under various high-dimensional time series models. An application to spatio-temporal data illustrates the method's utility for non-Euclidean observations.

Citations

• Testing Serial Independence of Object-Valued Time Series
• Rank Based Tests for High Dimensional White Noise
• Hypothesis testing for high-dimensional time series via self-normalization
• Distance-based and RKHS-based Dependence Metrics in High Dimension
• On testing for high-dimensional white noise
• On a measure of lack of fit in time series models

Related

• Testing Serial Independence of Object-Valued Time Series
• Testing mutual independence in high dimension via distance covariance
• Free congruence: an exploration of expanded similarity measures for time series data
• Robust Two-Sample Inference under Serial Dependence
• A Shift Test for Independence in Generic Time Series