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.

翻译：我们提出了一种用于检验序列独立性的非参数方法，该方法通过滞后依赖权重聚合观测值的成对相似性。所构建的统计量对包括非线性及非相关替代假设在内的多种时间依赖形式均具有较强检验功效，且适用于超高维及非欧几里得数据。我们分别在置换零假设与总体零假设下推导了统计量的渐近正态性，并在经典大样本及高维低样本量（HDLSS）体系中证明了检验的一致性。因此，该检验首次为HDLSS框架下的序列独立性提供了理论功效保证。数值模拟显示该方法在多种替代假设下均能保持准确的检验水平并表现出较强的检验功效，在各种高维时间序列模型中较现有方法具有显著的功效提升。对时空数据的应用案例进一步展示了该方法处理非欧几里得观测值的实用性。