# Typhoon Track Prediction Based on Deep Learning
## 2 Materials and Methodology
### Typhoon Path Prediction Model Based on C-LSTM Network
#### 2.2.1 Multi-Feature Selection
In this paper, the auto.arima() function of R language was used for automatic order determination. After determining the optimal lag order, the model was constructed for the six series that were smooth only after the first-order difference, and the residuals were tested separately by the ADF test, and it was found that their \(p\)-values were all less than 0.01, i.e., all these six series had cointegration relationship, and they could be tested for Granger causality. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Meteorological Variables** & \(p\)**-Value** & **Meteorological Variables** & \(p\)**-Value** \\ \hline CAT & **<0.01** & R_LONG & 0.06493 \\ LAT & **<0.01** & R_SHORT & 0.08179 \\ LON & **<0.01** & POCI & 0.6398 \\ TRACK\_TYPE & **<0.01** & POCI & **<0.01** \\ DIST2 LAND & **<0.01** & RMW & **<0.01** \\ LANDFALL & **<0.01** & EYE & 0.03763 \\ WIND & **<0.01** & GUSTS & 0.4172 \\ PRES & 0.5646 & SPEED & **<0.01** \\ R\_DIR & **<0.01** & DIR & **<0.01** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of smoothness tests of typhoon meteorological variables. 3. Granger causality test. To determine whether the above 18 meteorological variables affect the typhoon path, we need to test whether there is Granger causality between each meteorological variable and typhoon longitude and latitude in turn. (1) Test the hypothesis \"H0: X is not a Granger cause of Y change\". The two regression equations in Equations (6) and (7) are first estimated. Unconstrained regression Equation \(u\):  
\[Y_{t}=\alpha_{0}+\sum_{i=1}^{p}\alpha_{i}Y_{t-1}+\sum_{i=1}^{q}\beta_{i}X_{t-1 }+\varepsilon_{t} \tag{6}\]  
Constrained regression equation \(r\):  
\[Y_{t}=\alpha_{0}+\sum_{i=1}^{p}\alpha_{i}Y_{t-1}+\varepsilon_{t} \tag{7}\]  
where \(\alpha_{0}\) denotes the constant term, \(p\) and \(q\) denote the maximum lag order of variables X and Y, respectively, and \(\varepsilon_{t}\) denotes white noise. Then, the residual sums of squares \(RSS_{u}\) and \(RSS_{r}\) of the above two equations are used to construct the statistic \(F\), which is calculated as Equation (8). \[F=\frac{(RSS_{u}-RSS_{r})/q}{RSS_{u}/(n-p-q-1)} \tag{8}\]  
where \(n\) denotes the sample size. If \(F\geq F_{a}\), then the original hypothesis is rejected. If \(F<F_{a}\), then the original hypothesis cannot be rejected. (2) Repeat step (1) by swapping the positions of variables Y and X. Test the hypothesis \"H0: Y is not the Granger cause of the change in X\". (3) When the hypothesis \"H0: Y is not the Granger cause of the change in X\" is valid and the hypothesis \"H0: X is not the Granger cause of the change in Y\" is not valid, we can  
Figure 4: ACF and PACF plots of the meteorological variable CAT. obtain the conclusion that \"variable X is the Granger cause of variable Y\" is obtained when both the assumptions \"H0: Y is not the Granger cause of X\" and \"H0: X is not the Granger cause of Y\" are satisfied. In this paper, the lag period is set to 2, and the original hypothesis indicates that this meteorological variable is not the Granger cause of typhoon latitude and longitude, which \(F\) is obtained as shown in Table 4.  
When the value of \(F\) is significantly smaller than the confidence level (1%), i.e., when \(F<0.01\), the original hypothesis is rejected, and this meteorological variable is the Granger cause of typhoon longitude and latitude. Therefore, the meteorological variables DIST2 LAND, LANDFALL, WIND, SPEED, and DIR are the Granger causes of typhoon longitude. The meteorological variables CAT, WIND, PRES, and DIR are the Granger causes of typhoon latitude.