Analysis of stock market indices through multidimensional scaling

Abstract

Two similarity measures are employed to compare historic stock market indices over time. The more traditional Euclidean similarity is employed to provide a reference. As a comparison, dynamic time warping is introduced as a similarity measure. Multidimensional scaling is employed to compare these dissimilarities on 15 financial indices sampled daily over a 10-year period. In addition to investigating the whole period, 1-year tranches are also considered. This analysis is compared to a recent study of Machado et al. [Analysis of stock market indices through multidimensional scaling, Commun. Nonlinear Sci. Numer. Simul. 16(12) (2011), pp. 4610–4618], who examined these same indices using correlation as a similarity measure. It is suggested that this approach may be problematic. Doubt is also cast on the efficacy of the ‘histogram’ similarity they also propose.

Keywords:

• dynamic time warping
• multidimensional scaling
• Procrustes analysis
• time series