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Register a new userTopological Properties of Stock Networks Based on Random Matrix Theory in Financial Time Series
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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.
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In this study, we have investigated factors of determination which can affect the connected structure of a stock network. The representative index for topological properties of a stock network is the number of links with other stocks. We used the multi-factor model, extensively acknowledged in financial literature. In the multi-factor model, common factors act as independent variables while returns of individual stocks act as dependent variables. We calculated the coefficient of determination, which represents the measurement value of the degree in which dependent variables are explained by independent variables. Therefore, we investigated the relationship between the number of links in the stock network and the coefficient of determination in the multi-factor model. We used individual stocks traded on the market indices of Korea, Japan, Canada, Italy and the UK. The results are as follows. We found that the mean coefficient of determination of stocks with a large number of links have higher values than those with a small number of links with other stocks. These results suggest that common factors are significantly deterministic factors to be taken into account when making a stock network. Furthermore, stocks with a large number of links to other stocks can be more affected by common factors.
The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.
This paper has been withdrawn by the authors.
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