# Exploring the Dynamics of Global Plate Motion Based on the Granger Causality Test
## 3 Data Analysis and Results
### Stationarity Test of Energy Release  
The following procedure employs the annual energy release after transformation into natural logs from 1904 to 2014 of 28 plate boundaries, as shown in Figure 3. The augmented Dickey-Fuller (ADF) test is the most frequently used unit root test to examine the stationarity of time series. It is an extension of the DF test, which is a parametric approach originally proposed by [PERSON] and [PERSON] [55,56]. Although the method is questioned by some studies, it is still one of the most widely used methods. In addition, [PERSON] anticipated that many unit root test methods would support the same conclusion if a sufficient sample size was used. Therefore, ADF was used to test the stationarity of the energy release at all plate boundaries, and the results are presented in Table 2.  
Figure 2: Map of world’s earthquake events and plate boundaries. Black dots are earthquakes with magnitudes greater than 5.6, the red text gives the names of plates (AF: Africa, AN: Antarctica, SO: Somalia, IN: India, AU: Australia, NZ: Nazca, EU: Eurasia, PA: Pacific, SA: South America, PS: Philippine Sea, NA: North America, AR: Arabia), red lines show plate boundaries, and purple text gives the names of plate boundaries.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline Boundary name & NA-PA & NA-PA & NA-PA & AU-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & AU-AU & AF-OR \\ \hline Earthquake Number & 4470 & 283 & 275 & 6005 & 1027 & 1560 & 1609 & 256 & 405 & 409 & 106 & 408 & 56 & 107 \\ Energy Release & 17.5 \(\times\) 10\({}^{22}\) & 22.1 \(\times\) 10\({}^{12}\) & 17.3 \(\times\) 10\({}^{20}\) & 5.6 \(\times\) 10\({}^{20}\) & 22.1 \(\times\) 10\({}^{12}\) & 15.1 \(\times\) 10\({}^{12}\) & 14.8 \(\times\) 10\({}^{12}\) & 3.28 \(\times\) 10\({}^{12}\) & 5.39 \(\times\) 10\({}^{12}\) & 3.81 \(\times\) 10\({}^{12}\) & 28.3 \(\times\) 10\({}^{12}\) & 28.4 \(\times\) 10\({}^{12}\) \\ Boundary name & NA-PA & AR-U & NA-PN & SO-AU & SO-AU & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN & NA-PN \\ \hline Earthquake Number & 84 & 307 & 27 & 57 & 65 & 84 & 121 & 136 & 91 & 1507 & 305 & 68 & 2071 & 422 \\ Energy Release & 72.4 \(\times\) 10\({}^{20}\) & 24.5 \(\times\) 10\({}^{20}\) & 9.0 \(\times\) 10\({}^{20}\) & 25.6 \(\times\) 10\({}^{20}\) & 25.2 \(\times\) 10\({}^{20}\) & 5.6 \(\times\) 10\({}^{20}\) & 3.89 \(\times\) 10\({}^{20}\) & 12.7 \(\times\) 10\({}^{12}\) & 2.99 \(\times\) 10\({}^{12}\) & 5.2 \(\times\) 10\({}^{12}\) & 12.5 \(\times\) 10\({}^{12}\) & 3.39 \(\times\) 10\({}^{12}\) & 2.87 \(\times\) 10\({}^{12}\) & 2.85 \(\times\) 10\({}^{12}\) & 2.85 \(\times\) 10\({}^{12}\) \\ \hline \end{tabular}
\end{table}
Table 1: Earthquakes and energy release at plate boundaries.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline Boundary name & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PA & NA-PN & NA-PN \\ \hline Earthquake Number & 4470 & 283 & 275 & 6005 & 1027 & 1560 & 1609 & 256 & 405 & 409 & 106 &  
The null hypothesis that the time series contains a unit root can be rejected for all of the series at the 1% level. This result means that the annual energy release at all plate boundaries is \(I(0)\) in nature. The results of the stationarity test reported in Table 2 show that all variables are confirmed to be stationary at the 0.05 level.