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

TL;DR

This paper introduces a hierarchical measure of frustration in complex systems, applied to the U.S. Intermarket, using correlation coefficients as entanglement indicators to analyze systemic dynamics over several decades.

Contribution

It extends the concept of frustration to n-ary relations and develops a hierarchy of frustrations as supplementary indices for complex system analysis.

Findings

Hierarchy of frustrations correlates with market dynamics.

The model captures systemic stress levels over time.

Application to U.S. Intermarket data reveals meaningful patterns.

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.