Hierarchy of Frustrations as Supplementary Indices in Complex System Dynamics, Applied to the U.S. Intermarket

Abstract

Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is chosen where the correlation coefficient of intermarket sectors plays the role of entanglement measure. In each hierarchy level the frustration and the transitivity are interpreted as values of an order of measure for corresponding subsystem. The derived theory is applied to 1983-2012 data of the U.S. Intermarket.