Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 819503, 14 pages
Research Article

Analysis of Stock Market Indices with Multidimensional Scaling and Wavelets

1Department of Electrical Engineering, Institute of Engineering, 4200-072 Porto, Portugal
2Faculty of Engineering and Natural Sciences, Lusofona University, 1749-024 Lisboa, Portugal
3Faculty of Economics and Management, Lusofona University, 1749-024 Lisboa, Portugal

Received 20 January 2012; Accepted 12 March 2012

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2012 J. Tenreiro Machado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Stock market indices (SMIs) are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling (MDS). Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.