Clustering of time series using quantile autocovariances

Abstract

Time series clustering is an active research topic with applications in many fields. Unlike conventional clustering on multivariate data, time series often change over time so that the similarity concept between objects must take into account the dynamic of the series. In this paper, a distance measure aimed to compare quantile autocovariance functions is proposed to perform clustering of time series. Quantile autocovariances provide information about the serial dependence structure at different pairs of quantile levels, require no moment condition and allow to identify dependence features that covariance-based methods are unable to detect. Results from an extensive simulation study show that the proposed metric outperforms or is highly competitive with a range of dissimilarities reported in the literature, particularly exhibiting high capability to cluster time series generated from a broad range of dependence models. Estimation of the optimal number of clusters is also addressed. For illustrative purposes, our methodology is applied to a real dataset involving financial time series.