Dynamics of the market states in the space of correlation matrices with applications to financial markets

TL;DR

This paper reviews the evolution and recent advances in understanding market states through correlation matrices, exploring trajectory analysis, symbolic dynamics, and clustering within a random matrix framework.

Contribution

It provides a comprehensive overview of past and recent methods for analyzing market states via correlation matrices, including new approaches for trajectory and cluster analysis.

Findings

Correlation-based market states have evolved over the past decade.

Recent methods include trajectory analysis and symbolic dynamics.

Clustering in random matrix theory offers new insights into market states.

Abstract

The concept of states of financial markets based on correlations has gained increasing attention during the last 10 years. We propose to retrace some important steps up to 2018, and then give a more detailed view of recent developments that attempt to make the use of this more practical. Finally, we try to give a glimpse to the future proposing the analysis of trajectories in correlation matrix space directly or in terms of symbolic dynamics as well as attempts to analyze the clusters that make up the states in a random matrix context.