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Clustering multivariate time series using energy distance

Author

Listed:
  • Richard A. Davis
  • Leon Fernandes
  • Konstantinos Fokianos

Abstract

A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Székely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure the separation between the finite‐dimensional distributions for the component time series. Once the pairwise dissimilarity matrix is calculated, a hierarchical clustering method is then applied to obtain the dendrogram. This procedure is completely nonparametric as the dissimilarities between stationary distributions are directly calculated without making any model assumptions. In order to justify this procedure, asymptotic properties of the energy distance estimates are derived for general stationary and ergodic time series. The method is illustrated in a simulation study for various component time series that are either linear or nonlinear. Finally, the methodology is applied to two examples; one involves the GDP of selected countries and the other is the population size of various states in the U.S.A. in the years 1900–1999.

Suggested Citation

  • Richard A. Davis & Leon Fernandes & Konstantinos Fokianos, 2023. "Clustering multivariate time series using energy distance," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 487-504, September.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:5-6:p:487-504
    DOI: 10.1111/jtsa.12688
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    References listed on IDEAS

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    Cited by:

    1. Alessia Benevento & Fabrizio Durante & Roberta Pappadà, 2025. "Comonotonic‐Based Time Series Clustering With Constraints: A Review and a Conceptual Framework," Environmetrics, John Wiley & Sons, Ltd., vol. 36(8), December.

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