Exploratory classification of time-series

In this paper, an exploratory hierarchical method to classify variables is introduced as an alternative to principal component analysis when dealing with stock-exchange price time-series. The method is based on a particular principal component analysis applied to pairs of variables, each one associated to a group to be merged. Applied to time-series, this method reveals advantageous, since it helps in defining the number of groups and their composition, while providing a factorial structure of both the hierarchy's nodes and the partition groups. Moreover, all the issued factors, which are weighted sums of the original variables forming the groups, result in easily interpretable representative variables of them. As a case study, the method is applied to a set of Brazilian financial stock price time-series, providing representative series for each of the five groups of the proposed partition. This result complements the information on the data set provided by principal component analysis, limited to the usual orthogonal factors, each one representing an independent source of variation. It is likely that the use of such classification method may help both in deepening the knowledge of a market structure and the modelling of the different time-series, based on the modelling of their representative one.