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Stochastic Flow Diagrams

23 Pages Posted: 16 Jan 2014 Last revised: 27 May 2014

Neil J. Calkin

Clemson University

Marcos Lopez de Prado

Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC

Date Written: February 8, 2014


Inspired by visualization techniques à la Feynman, 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: Time Series, Graph Theory, Topology, Financial Flows, Macro Trading

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

Calkin, Neil J. and Lopez de Prado, Marcos, Stochastic Flow Diagrams (February 8, 2014). Algorithmic Finance 2014, 3:1-2, 21-42. Available at SSRN: or

Neil J. Calkin

Clemson University ( email )

101 Sikes Ave
Clemson, SC 29634
United States


Marcos Lopez de Prado (Contact Author)

Guggenheim Partners, LLC ( email )

330 Madison Avenue
New York, NY 10017
United States


Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States


Harvard University - RCC ( email )

26 Trowbridge Street
Cambridge, MA 02138
United States


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