Dynamic time warping as a similarity measure: applications in finance

Abstract

This paper presents the basic DTW-algorithm and the manner it can be used as a similarity measure for two different series that might differ in length. Through a simulation process it is being showed the relation of DTW-based similarity measure, dubbed ?_DTW, with two other celebrated measures, that of the Pearson’s and Spearman’s correlation coefficients. In particular, it is shown that ?_DTW takes lower (greater) values when other two measures are great (low) in absolute terms. In addition a dataset composed by 8 financial indices was used, and two applications of the aforementioned measure are presented. First, through a rolling basis, the evolution of ?_DTW has been examined along with the Pearson’s correlation and the volatility. Results showed that in periods of high (low) volatility similarities within the examined series increase (decrease). Second, a comparison of the mean similarities across different classes of months is being carried. Results vary, however a statistical significant greater similarity within Aprils is being reported compared to other months, especially for the CAC 40, IBEX 35 and FTSE MIB indices.