Topological Network Analysis Based on Dissimilarity Measure of Multivariate Time Series Evolution in the Subprime Crisis

Abstract

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. Int. J. Financial Stud. 2018, 6, 47 2 of 16 management of assets, is considered to be an important topic in this regard. From a statistical physics perspective, correlation analysis between financial objects has developed in various approaches, such as the multi-fractal analysis theory, random matrix theory, and correlation network-based approaches (e.g., the planar maximally filtered graph, the minimum spanning tree (MST), and the correlation threshold approaches). Particularly, as Mantegna (1999) initially proposed the network analysis tool of MST in the US stock market, the correlation network was applied for quantifying the interconnections in many financial markets, such as the commodity markets, foreign exchange (FOREX, FX) market, stock market, and equity markets.In financial markets, topological network analysis is a technical method that provides efficient tools to interpret market properties and structures (Mantegna 1999;Mantegna and Stanley 2000;Tumminello et al. 2005; Djauhari and Lee 2014). Network topology refers to the physical layout of a network. This approach has been investigated seriously by econophysicists to understand the structure of interrelated variables via network. It defines the way that different nodes are placed and are interconnected with each other. Alternately, technical topology networks describe how the data is transferred between these nodes. This is achieved by employing the well-known correlation network analysis approach. On the other hand, correlation network is usua...

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