# 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  
To reduce the model training time cost and to remove meteorological variables that have little influence on the typhoon path, the meteorological variables in the forecast factors are selected using Granger causality tests to achieve data dimensionality reduction before inputting the data into the forecast model. The process of Granger causality test is shown in Figure 3.  
In a time series, for two variables X and Y, variable X is considered to be the Granger cause of variable Y if variable X contributes to the prediction of variable Y and variable Y cannot explain future changes in variable X [26]. This causal relationship defined from a forecasting perspective is called the Granger relationship. 1. Stability test. Because an important prerequisite for the Granger causality test is that the time series must be smooth, before the Granger causality test, the time series needs to be tested for smoothness by unit root test, the common test method is the Augmented Dickey-Fuller test (ADF). If the series passes the ADF test, the Granger causality test can be performed. If the series does not pass the ADF test, it needs to be differenced until all series obey the same order of single integer to further confirm whether there is a cointegration relationship between the variables. The original hypothesis of the ADF test implies that the series is not stable when there is a unit root in the series. The series is stable only when the \(p\)-value is significantly smaller than the confidence level (1%), i.e., the original hypothesis is rejected. That is, when  
Figure 3: Process of Granger causality test. \(p\) < 0.01, the series is stable, and the Granger causality test can be performed. Otherwise, the first-order difference is required. The irrelevant variables of the dataset were removed, such as year, typhoon name, etc., and finally, all meteorological variables were obtained, containing 18 variables in total, and their smoothness test results are shown in Table 3.  
From Table 3, we can find that there are 12 series whose \(p\)-values are all less than 0.01, i.e., these 12 series have no unit root, are stable, and can be tested for Granger causality. While the \(p\)-values of PRES, R_LONG, R_SHORT, POCI, EYE, and GUSTS are all greater than 0.01, i.e., these 6 series are not stable and need to be first first-order differenced, i.e., using autoregression to extract the series determination information, and then test the smoothness. After the first-order differencing, the \(p\)-values of the above six series are all less than 0.01, i.e., the series is stable. 2. Cointegration test. After ensuring that all series are smooth, before conducting the Granger causality test, to check whether there is a cointegration relationship among the series and prevent the phenomenon of pseudo-regression, it is also necessary to conduct a cointegration test for the series with a first-order difference. (1) The optimal lag order is selected based on the minimum criterion of the Akaike information criterion (AIC) [27]. The AIC is calculated as Equation (5). \[\text{AIC}=2 lag+n\ln\biggl{(}\frac{RSS}{n}\biggr{)} \tag{5}\]  
where \(lag\) denotes the lag order, \(n\) denotes the sequence length, and \(RSS\) denotes the fit residuals. Usually, Autocorrelation Coefficient Function (ACF) and Partial Autocorrelation Coefficient Function (PACF) can be used for ranking. In addition, automatic orderings can be performed using programming languages. For a series \(\{x_{t}\}\), ACF can be used to measure the correlation between \(x_{t}\) and \(x_{t-k}\), while PACF can be used to measure the correlation between \(x_{t}\) and \(x_{t-k}\) with the lagged effect of \(x_{t-1},x_{t-2},\cdots,x_{t-k+1}\) removed. Taking the weather variable CAT in the dataset as an example, its ACF plot and PACF plot outputs are shown in Figure 4.  
(2) Test the stationarity of the residuals. If the residuals pass the ADF test, the series is cointegrated. Otherwise, it is not cointegrated.