Global stock markets: Analysis of complex networks evolution based on Information Theory quantifiers

OSVALDO A. ROSSO; LUCIANO ZUNINO; MARTÍN GÓMEZ RAVETTI

Ushuaia, Tierra del Fuego

Encuentro; DYSES 2012, VI International Meeting on Dynamics of Social and Economic Systems; 2012

Dyses Association

A novel methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers was proposed recently [L.C.Carpi, O.A.Rosso, P.Saco, M. Gómez Ravetti, Phys. Lett. A 375 (2011) 801]. In that work, the use of Statistical Complexity Measure [O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Plastino, M.A. Fuentes, Phys. Rev.Lett. 99 (2007) 154102] and the square root of the Jensen-Shannon divergence were proposed as a measure of dissimilarity and also to characterize the evolution of networks by means of their degree distribution. In the present contribution we study the global stock market evolution using the above mentioned network approach and their corresponding quantification based on Information Theory. The data employed in this study consists of free float-adjusted market capitalization stock indices of developed and emerging markets, constructed by Morgan Stanley Capital International (MSCI). Securities included in the indices are subject to minimum requirements in terms of market capitalization, free-float, liquidity, availability to foreign investors and length of trading. The dataset includes 23 markets classified as developed (Australia, Austria, Belgium,Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, United Kingdom and United States) and 23 markets classified as emerging (Argentina, Brazil, Chile, China, Czech Republic, Colombia, Egypt, Hungary, India, Indonesia, Israel, Korea, Malaysia, Mexico, Morocco, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand and Turkey).The time series consist of daily index prices, expressed in US dollars, between January 1995 and December 2010,corresponding to 4175 observations. In the event of days where there is a market holiday, the MSCI index construction methodology simply carries forward the index value from the previous business day. Each country was considered as a node in the network, and the topology of the network (that means if to nodes will be connected) was determined using the Spearman correlation between the time series associated to each node. Then the node degree distribution was evaluated using temporal windows without overlap of time length of one year. As we mention previously the data employed in this study covers the period from January 1995 to December 2010. This period witnessed the 1997 Asian currency crisis, the 2000 burst of the dot-com bubble, and the 2008-09 subprime mortgage crisis. We show that this crisis are well identified as a strong changes (peaks) in the time evolution of square Jensen-Shannon divergence for the probability distribution function (PDF) of the network and those corresponding to a totally random network, suggesting that the present network methodology and its quantification could be a nice tool for the quantitative analysis of the global stock markets.