Topological Properties of Stock Networks Based on Random Matrix Theory in Financial Time Series

TL;DR

This study analyzes the topological structure of stock networks across multiple markets using random matrix theory, revealing how eigenvalues influence network consistency and stock connectivity.

Contribution

It introduces a method to compare original and RMT-estimated stock networks, highlighting the role of eigenvalues in network formation across different markets.

Findings

Estimated networks increasingly align with original networks as correlation matrices reflect eigenvalue properties.

Largest eigenvalue significantly influences stock network structure.

Different stocks respond uniquely to eigenvalue-based network estimations.

Abstract

We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual stocks traded on the market indices of Korea, Japan, Canada, the USA, Italy, and the UK. The results are as follows. As the correlation matrix reflects the more eigenvalue property, the estimated stock network from the correlation matrix gradually increases the degree of consistency with the original stock network. Each stock with a different number of links to other stocks in the original stock network shows a different response. In particular, the largest eigenvalue is a significant deterministic factor in terms of the formation of a stock network.