## 3 Results and Discussions  
### Data Training  
Taking the monthly accident data from 2009 to 2019 as an example, the trend decomposition was not carried out first, and the accident number is directly used as the original time series, which is a non-stationary sequence. The smaller the \(p\)-value in the ADF test, the smoother the sequence, and the \(t\) should be less than the critical value. The EViews 10 software is used to perform time series tests. As shown in Table 2, the \(p\)-value of the first-order difference is much smaller than that of the second-order difference, and the difference between the test statistic and the critical value is larger, so the first-order difference is performed on the data. Since the auto-regressive moving average (ARMA) model differs by one difference from the ARIMA model, the ARMA modelwa used to predict the accident situation in 2019 for the time series after the difference, and the difference parameter d in the ARIMA model is also determined to be 1.  
Figure 4 shows the autocorrelation and partial autocorrelation plots after the series differential, with AC and PAC representing the autocorrelation coefficient and the partial autocorrelation coefficient, respectively, and the order of the delay period in portrait orientation. As can be seen from the figure, the sequence is significant in the 1 st order, and the descent from the 2 nd order is very large and becomes insignificant, but the significance suddenly increases around the 12 th order and then remains low in the state of significance. Therefore, the \(p\) and \(q\) values are initially set to 12, and the ARMA (12, 12) process is set. Then narrow the \(p\) and \(q\) values, in turn, give preference to the case where the AIC value is the smallest, and find the optimal combination ARMA (11, 12).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**First-Order Difference**} & \multicolumn{4}{c}{**Second-Order Difference**} \\ \hline \multirow{3}{*}{\(p\)-value = \(9.42\times 10^{-23}\)} & The test statistic (\(t\)) & \(-12.25\) & \multirow{3}{*}{\(p\)-value = \(7.86\times 10^{-17}\)} & The test statistic (\(t\)) & \(-9.75\) \\ \cline{2-5}  & Threshold value (\(1\%\)) & \(-3.49\) & & \(p\)-value = \(7.86\times 10^{-17}\) & Threshold value (\(1\%\)) & \(-3.49\) \\ \cline{2-5}  & Threshold value (\(5\%\)) & \(-2.89\) & & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \cline{2-5}  & Threshold value (\(10\%\)) & \(-2.58\) & & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of first-order differences versus second-order differential results.  
Figure 3: Flowchart of optimal order determination of fractional order grey accumulation model based on genetic algorithm.  
After the model is established, dynamic prediction [27] makes a multi-step forward prediction within the estimated interval and static prediction [28] makes each prediction by replacing the predicted value with the true value, and then one step forward. So, monthly data on accidents from 2009 to 2019 is trained and the number of accidents in each month in 2019 is predicted. The effect of the prediction is judged by the theory inequality coefficient, and the closer the value is to 0, the closer it is to the real data, and the better the prediction ability is proved. This means that the predicted values have greater volatility and a smaller proportion of variance, and the model can better simulate the fluctuations of the actual series. Thus, the inequality coefficient of dynamic prediction is 0.36, and the prediction effect is better. Static predicted values have greater volatility, but an unequal coefficient of 0.20 provides a better simulation of actual sequence fluctuations. As shown in Figure 5, the relative errors of the two methods for the prediction of accidents in 2019 are 3.10% and 8.28%, the correlation coefficients with the original data are 0.943 and 0.879, and the degree of fit R\({}^{2}\) exceeds 0.8.