Dynamics of quasi-stationary systems: Finance as an example

TL;DR

This paper introduces a combined cluster and stochastic process analysis method to understand complex high-dimensional dynamical systems, demonstrated on stock market data, revealing stability, transitions, and simplified representations.

Contribution

It presents a novel approach integrating clustering and stochastic analysis to characterize and simplify complex dynamical systems, with applications to financial data.

Findings

Identified stable states and transitions in stock market dynamics.

Developed criteria for merging clusters to reduce system complexity.

Recovered high-dimensional fixed points through optimization.

Abstract

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This combined method also allows to set up new criteria for merging clusters to simplify the complexity of the system. The low-dimensional approach allows to recover the high-dimensional fixed points of the system by means of an optimization procedure.