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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.
We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contrib
The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional poten
The topological properties of interbank networks have been discussed widely in the literature mainly because of their relevance for systemic risk. Here we propose to use the Stochastic Block Model to investigate and perform a model selection among se
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrel
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