State and group dynamics of world stock market by principal component analysis

TL;DR

This paper analyzes the dynamic interactions and structural changes in global stock markets from 1998 to 2012 using principal component analysis to identify market states, groupings, and their evolution during crises.

Contribution

It introduces a PCA-based method to detect market state changes and group dynamics, revealing stable European groups and shifts post-crisis.

Findings

European indices form a stable group over time

Market crises increase similarity among indices within groups

Post-crisis, European and American indices' differences decrease

Abstract

We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A change in market state is identified as a change in the first PC coefficients. Some indices do not show significant change of PCs in market state during crises. The indices exposed to the invested capitals in the stock markets are at the minimum level of risk. Using the first two PC coefficients, we identify indices that are similar and more strongly correlated than the others. We observe that the European indices form a robust group over the observation period. The dynamics of the individual indices within the group increase in similarity with time, and the dynamics of indices are more similar during the crises. Furthermore, the group formation of indices changes position in two-dimensional spaces due to crises. Finally, after a financial crisis, the difference of PCs between the European and American indices narrows.