Stability and Hierarchy of Quasi-Stationary States: Financial Markets as an Example

TL;DR

This paper combines geometric data analysis and stochastic modeling to study the non-stationary correlation structure of financial markets, revealing the dynamics, stability, and hierarchy of quasi-stationary states and linking them to historical events.

Contribution

It introduces a novel approach integrating geometric data analysis with stochastic models to analyze market states and their stability, providing new insights into market dynamics.

Findings

Identification of the dominating variable in market correlation dynamics

Explicit stochastic model for the evolution of market states

Connection between market state dynamics and historical market events

Abstract

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure. We identify the dominating variable and extract its explicit stochastic model. This allows us to establish a connection between its time evolution and known historical events on the market. We discuss the dynamics, the stability and the hierarchy of the recently proposed quasi-stationary market states.