Beyond pairwise correlation: capturing nonlinear and higher-order dependence with distance statistics

Authors
Affiliations

Benjamin Avanzi

Centre for Actuarial Studies, Department of Economics, University of Melbourne, Australia

Guillaume Boglioni Beaulieu

School of Risk and Actuarial Studies, University of New South Wales, Sydney, NSW 2052, Australia

Pierre Lafaye de Micheaux

School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Ho Ming Lee

Centre for Actuarial Studies, Department of Economics, University of Melbourne, Australia

Faculty of Economics and Business, KU Leuven, Belgium

Bernard Wong

School of Risk and Actuarial Studies, University of New South Wales, Sydney, NSW 2052, Australia

Rui Zhou

Centre for Actuarial Studies, Department of Economics, University of Melbourne, Australia

This is the home page for the code replicating the modelling and visualisation results for the paper Beyond pairwise correlation: capturing nonlinear and higher-order dependence with distance statistics, submitted to the 2026 All Actuaries Summit in Melbourne, Australia. In the paper, we introduce several distance-based dependence statistics, including the Hellinger correlation (Geenens and Lafaye de Micheaux 2022), distance covariance (Székely et al. 2007), joint distance covariance (Chakraborty and Zhang 2019), and the (multivariate) auto-distance correlation function for time series applications Zhou (2012). The illustrations for the Hellinger correlation, distance covariance, and the (multivariate) auto-distance correlation function are implemented in R and can be viewed by clicking here or the R page at the top. The illustration for joint distance covariance is implemented in Python and can be assessed here or by clicking the Python page at the top.

References

Chakraborty, Shubhadeep, and Xianyang Zhang. 2019. “Distance Metrics for Measuring Joint Dependence with Application to Causal Inference.” Journal of the American Statistical Association.
Fokianos, Konstantinos, and M Pitsillou. 2018. “Testing Independence for Multivariate Time Series via the Auto-Distance Correlation Matrix.” Biometrika 105 (2): 337–52.
Geenens, Gery, and Pierre Lafaye de Micheaux. 2022. “The Hellinger Correlation.” Journal of the American Statistical Association 117 (538): 639–53.
Székely, Gábor J, Maria L Rizzo, and Nail K Bakirov. 2007. Measuring and Testing Dependence by Correlation of Distances.
Zhou, Zhou. 2012. “Measuring Nonlinear Dependence in Time-Series, a Distance Correlation Approach.” Journal of Time Series Analysis 33 (3): 438–57.