Stochastic Flow Diagrams

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

See all articles by Neil Calkin

Neil Calkin

Clemson University

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; Abu Dhabi Investment Authority; True Positive Technologies

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

Neil Calkin

Clemson University ( email )

101 Sikes Ave
Clemson, SC 29634
United States


Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States


Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates


True Positive Technologies ( email )

United States


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