## 2 Materials and Methods
### Model Selection
#### 2.2.1 ARIMA Model  
The idea of the ARIMA model is to smooth out the original sequences that are not stationary, using the differential method to get a stationary sequence, which applies to the time series in this paper. The specific steps are as follows:  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline  & **The Actual Number of Accidents per Year** & **The New Number after a Sum of Monthly Accidents** & **The Actual Number of Deaths per Year** & **The New Number after a Sum of Monthly Deaths** \\ \hline The actual number of accidents per year & 1 & 0.903 & The actual number of deaths per year & 1 & 0.542 \\ \hline The new number after a sum of quarterly accidents & 0.947 & 0.990 & The new number after a sum of quarterly deaths & 0.905 & 0.738 \\ \hline \hline \end{tabular} Note: The correlation coefficients mentioned in this article are all Pearson correlation coefficients.  
\end{table}
Table 1: Pearson correlation coefficient of newly generated data after trend decomposition and real data.  
First, the original time series stationarity was determined by the augmented Dickey-Fuller test (ADF). This test is to determine whether there is a unit root in a sequence: if the sequence is stable, there is no unit root; Otherwise, there will be a unit root. The hypothesis of the ADF test is the existence of a unit root, and if the resulting significance test statistic is less than three confidence levels (10%, 5%, 1%), it should be (90%, 95%, 99%) confident to reject the null hypothesis.  
Secondly, the model is identified, and the parameters are estimated. The principle is to convert a nonstationary time series to a stationary time series and then regress the dependent variable only on its lag order and the present and lagging values of the random error term. In the ARIMA (\(p\), \(d\), \(q\)) model, \(d\) is the differential order; AR is autoregressive which is only suitable for predicting phenomena related to its previous period, \(p\) is the number of autoregressive terms; MA is the moving average which focuses on the accumulation of error terms and effectively eliminates random fluctuations in predictions, \(q\) is the number of moving average terms [21]. The model is represented as follows:  
\[(1-\sum_{i=1}^{p}\varnothing_{i}L^{i})(1-L)^{d}X_{t}=(1+\sum_{i=1}^{q}\theta_{ i}L^{i})\epsilon_{t} \tag{1}\]  
\(X_{t}\)\(\sim\)I (\(d\)): sequences with the integration of \(d\)-order; \((1-L)^{d}X_{t}\): differential operators. \(\varnothing_{i}\): autoregressive coefficients; \(\theta_{i}\): moving average coefficients; \(\epsilon_{t}\): Random items.  
Finally, the Akaike Information Criterion (AIC) which builds on the concept of entropy, can weigh the complexity of the estimated model against the goodness of the model fitting the data. The size of the AIC value is related to the number of parameters and samples. The fewer the parameters and the greater the number of samples result in the smaller the AIC value and the better the model. Thus, the purpose of the function is to find a model that best interprets the data while containing the fewest free arguments. Therefore, in order to avoid overfitting, the combination of parameters with the smallest AIC value should be selected as the optimal ARIMA model [22].