Independence Testing for Temporal Data

TL;DR

This paper introduces a new non-parametric method for testing independence between stationary temporal data, addressing limitations of existing approaches by providing a valid, consistent, and powerful test that estimates the optimal dependence lag.

Contribution

It proposes a novel temporal dependence statistic with block permutation that is asymptotically valid, universally consistent, and compatible with various dependence measures, eliminating multiple testing issues.

Findings

Method is asymptotically valid under proper assumptions.

Capable of estimating the optimal dependence lag.

Exhibits excellent power in simulation studies.

Abstract

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 an 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. Moreover, it is compatible with a rich family of distance and kernel based dependence measures, eliminates the need for multiple testing, and exhibits excellent testing power in various simulation settings.