## 2 Data  
We use closing price of stock market index from July 2, 1997 to December 30, 2016. In this paper, we used a set of time series that reconstructed the entire 20 years data into periods of 1, 4, 10, and 20-year. In economic cycle, 3-7 year is Kitchen cycle, 7-11 year is Juglar cycle, and 15-25 is called the Kuznets cycle [24]. Accordingly, we chose 4, 10, and 20-year in the economic cycle. In addition, the global efficiency was calculated from [PERSON] et al. [17] on a one-year cycle, so we selected a period of 1, 4, 10, and 20-years in this paper. That is, 20 sets of one-year (1997, 1998,..., 2016), five sets of four-year (1997-2000, 2001-2004, 2005-2008, 2009-2012, and 2013-2016), two sets of 10-year (1997-2006, 2007-2016), and one set of 20-year time series. We generated two types of data, return (\(r_{t}\)) and volatility (\(|r_{t}|\)), as following [25]. The difference of logarithms for consecutive closing indices is almost identical to the return. Additionally, the absolute value is approximately same as the volatility.  
\[\begin{array}{l}r_{t}=\log(P_{t+1})-\log(P_{t})\\ |r_{t}|=\left|\log(P_{t+1})-\log(P_{t})\right|\end{array} \tag{1}\]  
\(P_{t}\) is a stock price index at time \(t\) and \(P_{t+1}\) is one at time \(t+1\).  
Table 1 lists the names of surveyed stock markets. There are 24 markets of world-wide 19 countries. More specifically, 11 in Asia (eight countries), five in Europe (five countries), five in North America (two countries), three in South America (three countries), and two in Oceania (one country) were surveyed.  
Figure 1 shows the time series of stock price indices in 24 stock markets. There are markets that rise significantly overall, whereas there are markets that repeat rising and falling. It is common that the index plunged at the midpoint of the period (the 2008 global financial crisis). However, intuitively, it is hard to understand the correlations between these market indices. In general, the Pearson correlation coefficient is used to analyze the correlation between the two time series. However, the Pearson correlation coefficient was extraordinary high for the stock price index between countries, the temperature distribution between neighboring regions, and so on. Thus, the two time series appear to be self-evidently correlated.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No** & **Nation** & **Stock Market** & **No** & **Nation** & **Stock Market** \\ \hline
1 & Argentina & MERVALS & 13 & Korea1 & KOSPI \\
2 & Australia1 & AORD & 14 & Korea2 & KOSDAQ \\
3 & Australia2 & S\&P ASX200 & 15 & Mexico & IPC \\
4 & Brazil & IBOVESPA & 16 & Netherland & AEX \\
5 & Chile & IGPA & 17 & Pakistan & KSE100 \\
6 & France & CAC40 & 18 & Singapore & STI \\
7 & Germany & DAX & 19 & Taiwan & TAIMEX \\
8 & Hong Kong & HANGSENG & 20 & USA1 & DOW \\
9 & Hungary & BUX & 21 & USA2 & S\&P500 \\
10 & India & BSE SENSEX & 22 & USA3 & NASDAQ \\
11 & Indonesia & IDX & 23 & USA4 & DOW TRANS \\
12 & Japan & NIKKEI225 & 24 & UK & FTSE100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Surveyed global 24 stock market lists.  
Figure 1: Time series of stock 24 price indices of all surveyed stock markets.  
Thus, we will analyze the correlation between stock markets while using the detrended cross correlation analysis (DCCA) method to more strictly judge the correlation. The derived correlation is used to determine whether to connect the links between two nodes in network analysis.