韩美股市最小生成树的拓扑性质
Topological Properties of the Minimal Spanning Tree in Korean and American Stock Markets
摘要：
我们调查的一个因素，可以影响一个特定的股票在网络中的最小生成树（MST）的方法创建的股票之间的链接数，通过使用个人股票数据上列出的标准普尔500指数和KOSPI。在金融界广泛认可的套利定价模型（APM）中提到的常见因素中，建立了一个具有代表性的市场指数作为可能的因素。我们发现，相关性分布，$ρ_{ij}$，从标准普尔500指数的400只股票，显示了非常相似的韩国股市和那些偏离相关性分布的时间序列去除了替代方法的非线性。我们还表明，两个股票市场的MST的度分布遵循幂律分布，指数$ζ\sim$ 2.1，而消除非线性的时间序列的度分布遵循指数分布，指数$δ\sim 0.77$。此外，个股度k $i$和市场指数$M$之间的相关性$ρ_{iM}$遵循幂律分布$<ρ_{iM}(k) > \sim k^γ$，其指数分别为$γ_{\textrm{S&P500}} \approx 0.16$和$γ_{\textrm{KOSPI}} \approx 0.14$。因此，无论市场如何，与市场中的公共因素--市场指数密切相关的个体股票很可能位于股票之间网络的中心，而与市场指数弱相关的个体股票很可能位于网络的外部。
英文摘要：
We investigate a factor that can affect the number of links of a specific stock in a network between stocks created by the minimal spanning tree (MST) method, by using individual stock data listed on the S&P500 and KOSPI. Among the common factors mentioned in the arbitrage pricing model (APM), widely acknowledged in the financial field, a representative market index is established as a possible factor. We found that the correlation distribution, $ρ_{ij}$, of 400 stocks taken from the S&P500 index shows a very similar with that of the Korean stock market and those deviate from the correlation distribution of time series removed a nonlinearity by the surrogate method. We also shows that the degree distribution of the MSTs for both stock markets follows a power-law distribution with the exponent $ζ\sim$ 2.1, while the degree distribution of the time series eliminated a nonlinearity follows an exponential distribution with the exponent, $δ\sim 0.77$. Furthermore the correlation, $ρ_{iM}$, between the degree k of individual stock, $i$, and the market index, $M$, follows a power-law distribution, $<ρ_{iM}(k) > \sim k^γ$, with the exponent $γ_{\textrm{S&P500}} \approx 0.16$ and $γ_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of the markets, the indivisual stocks closely related to the common factor in the market, the market index, are likely to be located around the center of the network between stocks, while those weakly related to the market index are likely to be placed in the outside.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
