Effect of changing data size on eigenvalues in the Korean and Japanese stock markets

TL;DR

This study investigates how eigenvalues of stock market correlation matrices change with data size, revealing that the largest eigenvalue remains stable while others vary, using random matrix theory in Korean and Japanese markets.

Contribution

It provides new insights into eigenvalue behavior relative to data size and stock type, applying RMT to Asian stock markets.

Findings

Largest eigenvalue remains stable regardless of data size

Eigenvalues increase proportionally with the number of stocks

Other eigenvalues exhibit different features based on stock type

Abstract

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features.