A testing approach to clustering scalar time series

This article considers clustering stationary scalar time series using their marginal properties and a hierarchical method. Two major issues involved are to detect the existence of clusters and to determine their number. We propose a new test statistic for detecting whether a data set consists of multiple clusters and a new procedure to determine the number of clusters. The proposed method is based on the jumps, that is, the increments, in the heights of the dendrogram when a hierarchical clustering is applied to the data. We use autoregressive sieve bootstrap to obtain a reference distribution of the test statistics and propose an iterative procedure to find the number of clusters. The clusters found are internally homogeneous according to the test statistics used in the analysis. The performance of the proposed procedure in finite samples is investigated by Monte Carlo simulations and illustrated by some empirical examples. Comparisons with some existing methods for selecting the number of clusters are also investigated.