PT - JOURNAL ARTICLE
AU - Leibon, Gregory
AU - Pauls, Scott
AU - Rockmore, Daniel
AU - Savell, Robert
TI - Topological structures in the equities market network
AID - 10.1073/pnas.0802806106
DP - 2008 Dec 30
TA - Proceedings of the National Academy of Sciences
PG - 20589--20594
VI - 105
IP - 52
4099 - http://www.pnas.org/content/105/52/20589.short
4100 - http://www.pnas.org/content/105/52/20589.full
SO - Proc Natl Acad Sci USA2008 Dec 30; 105
AB - We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on “partition decoupled null models,” a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application, we analyze a correlation matrix derived from 4 years of close prices of equities in the New York Stock Exchange (NYSE) and National Association of Securities Dealers Automated Quotation (NASDAQ). In this example, we expose (i) a natural structure composed of 2 interacting partitions of the market that both agrees with and generalizes standard notions of scale (e.g., sector and industry) and (ii) structure in the first partition that is a topological manifestation of a well-known pattern of capital flow called “sector rotation.” Our approach gives rise to a natural form of multiresolution analysis of the underlying time series that naturally decomposes the basic data in terms of the effects of the different scales at which it clusters. We support our conclusions and show the robustness of the technique with a successful analysis on a simulated network with an embedded topological structure. The equities market is a prototypical complex system, and we expect that our approach will be of use in understanding a broad class of complex systems in which correlation structures are resident.