Topological structures in the equities market network

Abstract

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 four years of close prices of equities in the NYSE and NASDAQ. In this example we expose (1) a natural structure composed of two interacting partitions of the market that both agrees with and generalizes standard notions of scale (eg., sector and industry) and (2) 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. 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.

17 pages, 4 figures, 3 tables

References in corpus (4)

• A tool for filtering information in complex systems
• Synchronization reveals topological scales in complex networks
• Extracting the hierarchical organization of complex systems
• Systematic analysis of group identification in stock markets

Cited by in corpus (13)

• A roadmap for the computation of persistent homology
• Economic state classification and portfolio optimisation with application to stagflationary environments
• Information transfer between stock market sectors: A comparison between the USA and China
• Information flow networks of Chinese stock market sectors
• Introduction to correlation networks: Interdisciplinary approaches beyond thresholding
• Clustering by the way of atomic fission
• A Random Dot Product Model for Weighted Networks
• Nonlinear shifts and dislocations in financial market structure and composition
• Multiple dynamical time-scales in networks with hierarchically nested modular organization
• Partition Decoupling for Multi-gene Analysis of Gene Expression Profiling Data
• Self-adaption grey DBSCAN clustering
• A self-adaptive and robust fission clustering algorithm via heat diffusion and maximal turning angle
• Characteristic Characteristics