Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time-series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only linear associations, and requiring multiple tests and corrections. While many non-parametric and universally consistent dependence measures have recently been proposed, directly applying them to temporal data can inflate the p-value and result in invalid test. To address these challenges, this paper introduces the temporal dependence statistic with block permutation to test independence between temporal data. Under proper assumptions, the proposed procedure is asymptotically valid and universally consistent for testing independence between stationary time-series, and capable of estimating the optimal dependence lag that maximizes the dependence. Notably, it is compatible with a rich family of distance and kernel based dependence measures, eliminates the need for multiple testing, and demonstrates superior power in multivariate, low sample size, and nonlinear settings. An analysis of neural connectivity with fMRI data reveals various temporal dependence among signals within the visual network and default mode network.

翻译：时序数据在现代数据科学中日益普遍。一个基本问题是判断两个时间序列是否相关。现有方法往往存在局限性，例如依赖参数假设、仅能检测线性关联以及需要多重检验和校正。尽管近期涌现出许多非参数且普遍一致的依赖性度量方法，但直接将其应用于时序数据会导致p值膨胀并产生无效检验。为解决这些挑战，本文引入基于块置换的时序依赖性统计量来检验时序数据的独立性。在适当假设下，所提方法在检验平稳时间序列独立性时具有渐近有效性和普适一致性，并能估计使依赖性最大化的最优依赖滞后。值得注意的是，该方法兼容基于距离和核的丰富依赖性度量族，无需多重检验，并在多变量、小样本和非线性场景中展现出卓越的检验效能。基于fMRI数据的神经连接分析揭示了视觉网络与默认模式网络内部信号间多样的时序依赖关系。