Affiliations: [a] Department of Mathematical Sciences, Clemson University, Clemson, SC, USA | [b] Senior Managing Director, Guggenheim Partners, New York, NY, USA | [c] Research Affiliate, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Abstract: We introduce Stochastic Flow Diagrams (SFDs), a new mathematical approach to represent complex dynamic systems into a single weighted digraph. This topological representation provides a way to visualize what otherwise would be a morass of equations in differences. SFDs model the propagation and reverberation that follows a shock. For example, reverberation explains how a shock to a financial system can initiate a sequence of events that lead to a crash long after the occurrence of the shock. SFDs can simulate systems in stable, steady or explosive state. SFDs add Topology to the Statistical and Econometric toolkit. We believe that SFDs will help policy makers, investors and researchers communicate and discuss better the complexity of dynamic systems.
Keywords: 90C35, 90B15, 05C21, 62P05, 37M10
Keywords: Time series, graph theory, topology, financial flows, macro trading