Topological network analysis based on dissimilarity measure of multivariate time series evolution in the subprime crisis

Correlation network based on similarity is the common approach in financial network analyses where the Minimal Spanning Tree (MST) is used to filter the important information contained in the network. In this paper, by considering a distance matrix based on dissimilarities among multivariate time series of currency, a topological network was analyzed. A topological network can explain to what extent two or more multi-dimensional currency structures are different from each other. For this purpose, we examined the topological network of currency market from 2005 to 2011 in terms of the subprime crisis. After that, the multivariate time series evolution of MSTs were analyzed in terms of the structural changes for three periods (before, during, and after the crisis). Moreover, since the clusters of currencies in network analysis are due to regional factors, by considering each region, which is composed of a number of currencies, as an element on the financial system, we attempted to determine how a region interacts with the other regions in crisis periods. This motivated us to introduce a region-based network analysis of currencies. Since each region consisted of a different number of currencies compared to the others, the appropriate network analysis was in multivariate setting. Finally, the applications of the method were presented with the situation of a currencies crisis behavior. The results indicate significant changes in the topological structures of MSTs when their properties are compared to each other.