Hyper-ellipsoid Clustering of Time Series. A Case Study for Daily Stock Returns☆

Abstract In this article I present a dynamic clustering algorithm applied on financial time series data. The algorithm is inspired from the Gustafson-Kessel (GK) Clustering method in the sense that it identifies clusters of time series in the form of hyper-ellipsoids. The novelty of the algorithm resides in the dynamic search for clusters, depending on the analyzed data, without prior specification of a possible number of clusters. Also, there is no specification of a fixed distance from the cluster centers for points that do not belong to any cluster (noise points). The algorithm was applied to daily stock return data with the scope of establishing how well this technique would identify systemic events in the market that cannot usually be observed through classical statistical methods. The empirical results show that clustering efficiency depends on the time series length, the general trend in the market, and also to other qualitative characteristics of the time series, like industry sector.