 Recently, many studies indicated that the minimum spanning tree (MST) network whose metric distance is de?ned by using correlation coe?cients have strong implications on extracting infor- mation from return time series. However in many cases researchers may hope to investigate the strength of interactions but not the directions of them. In order to study the strength of interaction and connection of ?nancial asset returns we propose a modi?ed minimum spanning tree network whose metric distance is de?ned from absolute cross-correlation coe?cients. We had investigated 69 daily ?nancial time series, which constituted by 3 types ?nance assets(29 stock market indica- tor time series , 21 currency futures price time series and 19 commodity futuresprice time series). Empirical analyses show that the MST network of returns is time-dependent in overall structure, while same type ?nancial assets usually keep stable inter-connections. Moreover each asset in same group show similar economic characters. In other words, each group concerned with one kind of traditional ?nancial commodity. In addition, we ?nd the time-lag between stock market indicator volatility time series and EUA (EU allowances) , WTI (West Texas Intermediate)volatility time series. The peak of cross-correlation function of  volatility time series between EUA (or WTI) and stock market indicators show a signi?cant time shift (> 20days) from 0.
In a highly interdependent economic world, the nature of relationships between financial entities is becoming an increasingly important area of study. Recently, many studies have shown the usefulness of minimal spanning trees (MST) in extracting interactions between financial entities. Here, we propose a modified MST network whose metric distance is defined in terms of cross-correlation coefficient absolute values, enabling the connections between anticorrelated entities to manifest properly. We investigate 69 daily time series, comprising three types of financial assets: 28 stock market indicators , 21 currency futures , and 20 commodity futures. We show that though the resulting MST network evolves over time, the financial assets of similar type tend to have connections which are stable over time. In addition, we find a characteristic time lag between the volatility time series of the stock market indicators and those of the EU CO2 emission allowance (EUA) and crude oil futures (WTI). This time lag is given by the peak of the cross-correlation function of the volatility time series EUA (or WTI) with that of the stock market indicators , and is markedly different (> 20 days) from 0, showing that the volatility of stock market indicators today can predict the volatility of EU emissions allowances and of crude oil in the near future.
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indicated that the minimum spanning tree
have shown the usefulness of minimal spanning trees
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network whose metric distance is de?ned by using correlation coe?cients have strong implications on extracting infor- mation from return time series. However in many cases researchers may hope to investigate the strength of interactions but not the directions of them. In order to study the strength of interaction and connection of ?nancial asset returns
in extracting interactions between financial entities. Here,
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which constituted by 3 types ?nance assets(29 stock market indica- tor time series
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price time series and 19 commodity futuresprice time series). Empirical analyses show that the MST network of returns is time-dependent in overall structure, while same type ?nancial assets usually keep stable inter-connections. Moreover each asset in same group show similar economic characters. In other words, each group concerned with one kind of traditional ?nancial commodity. In
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find a characteristic time lag between the
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