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Statistical Investigation of Connected Structures of Stock Networks in Financial Time Series

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.