Research Links: Correlation Networks



Evolution of worldwide stock markets, correlation structure and correlation based graphs [arXiv]

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 – Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, correlation based graphs and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of correlation of market indices. We introduce a measure of mutual information based on link co-occurrence in networks, in order to detect the fast dynamics of successive changes of correlation based graphs in a quantitative way.


A network perspective of the stock market [Hong Kong Polytechnic University]

Complex networks are constructed to study correlations between the closing prices for all US stocks that were traded over two periods of time (from July 2005 to August 2007; and from June 2007 to May 2009). The nodes are the stocks, and the connections are determined by cross correlations of the variations of the stock prices, price returns and trading volumes within a chosen period of time. Specifically, a winner-take-all approach is used to determine if two nodes are connected by an edge. So far, no previous work has attempted to construct a full network of US stock prices that gives full information about their interdependence. We report that all networks based on connecting stocks of highly correlated stock prices, price returns and trading volumes, display a scalefree degree distribution. The results from this work clearly suggest that the variation of stock prices are strongly influenced by a relatively small number of stocks. We propose a new approach for selecting stocks for inclusion in a stock index and compare it with existing indexes. From the composition of the highly connected stocks, it can be concluded that the market is heavily dominated by stocks in the financial sector.


Systemic risk and causality dynamics of the world international shipping market [Boston University]

Various studies have reported that many economic systems have been exhibiting an increase in the correlation between different market sectors, a factor that exacerbates the level of systemic risk. We measure this systemic risk of three major world shipping markets, (i) the new ship market, (ii) the second-hand ship market, and (iii) the freight market, as well as the shipping stock market. Based on correlation networks during three time periods, that prior to the financial crisis, during the crisis, and after the crisis, minimal spanning trees (MSTs) and hierarchical trees (HTs) both exhibit complex dynamics, i.e., different market sectors tend to be more closely linked during financial crisis. Brownian distance correlation and Granger causality test both can be used to explore the directional interconnectedness of market sectors, while Brownian distance correlation captures more dependent relationships, which are not observed in the Granger causality test. These two measures can also identify and quantify market regression periods, implying that they contain predictive power for the current crisis


Dynamic spanning trees in stock market networks: The case of Asia-Pacific [Banco Central do Brasil]

This article proposes a new procedure to evaluate Asia Pacific stock market interconnections using a dynamic setting. Dynamic Spanning Trees (DST) are constructed using an ARMA-FIEGARCH-cDCC process. The main results show that: 1. The DST significantly shrinks over time; 2. Hong Kong is found to be the key financial market; 3. The DST has a significantly increased stability in the last few years; 4. The removal of the key player has two effects: there is no clear key market any longer and the stability of the DST significantly decreases. These results are important for the design of policies that help develop stock markets and for academics and practitioners.


DynamiC asset trees and BlaCk Monday [arXiv]

The minimum spanning tree, based on the on concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree an be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called the  ‘central node’. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.