2023/05/15 by Zhaolu Liu, Liu, Zhaolu, Robert L. Peach +7 · 1 citation
Economics, Econometrics and Finance · Biochemistry, Genetics and Molecular Biology · Environmental Science · #Complex Systems and Time Series Analysis #Metabolomics and Mass Spectrometry Studies #Ecosystem dynamics and resilience
paper · pdf · doi:10.48550/arxiv.2305.08529
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, neuroscience, 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.