Topological structures in the equities market network

TL;DR

This paper introduces a novel multiscale topological analysis method for complex networks, applied to stock market data, revealing natural structures and patterns like sector and industry groupings, and sector rotation.

Contribution

The paper presents Partition Decoupled Null Models, a new approach for multiresolution topological analysis of correlation networks, generalizing existing models and uncovering market structures.

Findings

Identified two interacting partitions corresponding to market sectors and industries.

Revealed topological patterns reflecting sector rotation in stock markets.

Provided a multiresolution framework for analyzing complex correlation structures.

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.