## 4 _Atb_ Analysis Method and Result
### Model Development  
#### 4.3.1 Model Development Process  
The ARIMA model was used for analysis and prediction of the univariate time series data of _ATB_ with uniform interval.  
\[W_{t}=\mu+\frac{\theta(B)}{\varphi(B)}a_{t}\]  
where,  
\(t\): the indexes time  
\(W_{t}\): the response series  
\(\mu\): the mean term  
\(\varphi(B)\): the autoregressive operator  
\(\theta(B)\): the moving average operator  
\(a_{t}\): the independent disturbance  
The analysis was performed in three stages. In the first stage, the identification stage, the stationary status of the time series data was confirmed, and all four groups (daytime drivers aged under 60, daytime drivers aged 60 or above, nighttime drivers aged under 60, and nighttime drivers aged 60 or above) were fixed in the first differences (stationary). One or more models were tentatively selected using data on the occurrence of a dangerous event while driving for the period of one year. Accurate estimates of the parameters of the models were then obtained with the least-squares method.  
Second, the ARIMA model was applied on the estimation stage and the accuracy of the model was tested based on diagnostic statistics. The optimal model was selected based on the following diagnosis.  
1. Low Akaike information criteria (AIC). AIC is estimated by AIC = (\(-2\)log L + 2(p + q), where \"p\" is the autoregressive parameter and \"q\" is the moving average parameter. \"L\" is the likelihood function.
2. Insignificance of autocorrelations for residuals. If a model is an adequate representation of a time series, it should capture all the correlations in the series, and the white noise residuals should be independent of each other.
3. Significance of the parameters. Significance tests for parameter estimates indicate whether some terms in the model might be unnecessary.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & **Vehicle** & \multirow{2}{*}{**Corporation**} & \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Time**} & **GPS X** & **GPS Y** & \multirow{2}{*}{**ADAS\_CODE**} & \multirow{2}{*}{**Speed**} & \multirow{2}{*}{**Shift**} \\  & **Number** & & & & **Coordinate** & & & & \\ \hline A-2509437 & 6831 & A-Sang & 20180410 & 5347 & 37.65004 & 127.0555 & Forward Collision & 90 & Night \\ A-2509438 & 6831 & A-Sang & 20180410 & 5356 & 37.65187 & 127.0552 & Right-lane departure & 85 & Night \\ A-2509440 & 6831 & A-Sang & 20180410 & 10,007 & 37.65899 & 127.0532 & Collision Warning & 65 & Night \\ A-2509441 & 6831 & A-Sang & 20180410 & 10,045 & 37.65179 & 127.0553 & Left-lane departure & 83 & Night \\ A-2512363 & 6831 & A-Sang & 20180427 & 35,436 & 37.65553 & 127.0549 & Forward Collision & 96 & Night \\ A-2512365 & 6831 & A-Sang & 20180427 & 35,728 & 37.66279 & 127.0449 & Right-lane departure & 76 & Night \\ A-2518297 & 6836 & A-Sang & 20180414 & 224,138 & 37.63483 & 127.024 & Pedestrian collision & 10 & Night \\ \hline \hline \end{tabular}
\end{table}
Table 7: Sample of IoT log data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Working Hours** & **No. of Participants** \\ \hline Daytime drivers aged under 60 & 06:00–18:00 & 19 \\ Daytime drivers aged 60 or above & 18:00–06:00 & 18 \\ Nighttime drivers aged under 60 & 06:00–18:00 & 21 \\ Nighttime drivers aged 60 or above & 18:00–06:00 & 12 \\ Sum & & 70 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Working hours and number of people in the _ATB_ analytics group.  
Third, in the forecasting stage, future values of the time series after one year were forecasted.