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# Measuring critical transitions in financial markets

## Details

**Authors** Jan Jurczyk, Thorsten Rehberg, Alexander Eckrot, Ingo Morgenstern

**Year** 2017

**Publisher** Scientific Reports

**Kind of work** article

**Discipline** Complexity Science

**Secondary disciplines** Economics, Physics

**Applied** false

[Read it at the publisher](https://doi.org/10.1038/s41598-017-11854-1) 
10.1038/s41598-017-11854-1

## In authors' words

### Abstract

Tipping points in complex systems are structural transitions from one state to another. In financial markets these critical points are connected to systemic risks, which have led to financial crisis in the past. Due to this, researchers are studying tipping points with different methods. This paper introduces a new method which bridges the gap between real-world portfolio management and statistical facts in financial markets in order to give more insight into the mechanics of financial markets.

### What they set out to do (purpose)

To develop a method for detecting structural tipping-point transitions in financial markets by combining portfolio-similarity analysis with eigenvalue decomposition of market correlation structure.

### Who or what was studied (sample)

S&P 500 index constituent data, 2000-2016.

### How they did it (methods)

Eigenvalue decomposition of the time-varying correlation matrix of stock returns to track portfolio-similarity structure over time, identifying discrete state changes and relating them to subsequent trading-volume behavior.

### What they found (results)

The eigenvalue-based method detected major structural state changes in the S&P 500 correlation structure coinciding with the October 2008 and October 2011 market crises, and in the week following a state change involving more than two shifted eigenvectors, trading volume changes were measurably linked to that transition.

## Commentary

### In short

The finding shows the Distinctions pattern in that it identifies discrete before and after market states separated by a structural transition, the Systems pattern in that the market is treated as a whole whose collective eigenvector structure emerges from correlations among individual stocks, and the Relationships pattern in that a state change is linked to subsequent changes in trading volume.

**Patterns it shows** D, S, R

**Added** 2026-09-28

**How to cite this** Jan Jurczyk, Thorsten Rehberg, Alexander Eckrot, Ingo Morgenstern (2017). Measuring critical transitions in financial markets. Scientific Reports.