Clustering multivariate time series using energy distance

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