Interval-valued functional clustering based on the Wasserstein distance with application to stock data

Abstract

Interval-valued functional clustering is a novel approach for functional data analysis where each observation is represented by an interval. Existing interval-valued functional clustering methods typically rely on the interval-valued functional Hausdorff distance, which considers the upper and lower bounds of interval-valued functions but ignores the distribution of the original interval-valued data. This study proposes an interval-valued functional clustering method based on the Wasserstein distance to address this shortcoming. Taking into account the data distribution (i.e. the distribution’s centre and spread), this distance fully utilises the underlying data patterns. Furthermore, this study proposes a practical application of the interval-valued functional entropy method when multiple variables are used to comprehensively describe a phenomenon. Finally, an empirical example from the stock market demonstrates the proposed method’s effectiveness and superiority.