Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series

Felix Laumann, Robert L. Peach, Sara Vallejo Mengod, Zhaolu Liu, Mauricio Barahona

Publication date: 15 May 2023

Abstract: Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the

d

-variable Hilbert-Schmidt independence criterion (dHSIC) to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realisation time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate and socioeconomic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

Has companion code repository: https://github.com/barahona-research-group/dhsic_ts

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