## 4 Application
### eXtreme Gradient Boosting  
For streamlined parameter importance analysis, we classify the diverse densities derived from the original dataset into separate classification categories: 0 = very fluid, 1 = fluid, 2 = dense, 3 = very dense, 4 = congestion. The dataset, organized according to Table 3, contains information spanning the entirety of 2019. We partition the dataset into distinct sets for both training and testing stages during the evaluation process. Specifically, 70% of the dataset is earmarked for training purposes, while the remaining 30% is preserved for parameter evaluation. Data spanning January to March 2022 are processed for final analysis and predictions as presented in the model performance section. To optimize XGBoost's performance, parameter tuning is conducted using a cross-validation technique known as grid search with five folds. This involves exploring various parameter configurations within sensible ranges, as detailed in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Selected value** & **Options** \\ \hline max\_depth & 10 & 5, 7, 9, 10, 11 \\ eta & 0.3 & 0.1, 0.2, 0.3, 0.4 \\ gamma & 1 & 0.5, 1, 1.5, 2, 5 \\ subsample & 1 & 0.6, 0.8, 1 \\ objective & multi:softmax & - \\ num\_class & 5 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter matrix for XGBoost. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Section** & **Model** & **ME** & **RMSE** & **Independence** & **Homoscedasticity** & **Normality Test** \\  & & & **Test (\(p\)-Value)** & **Test (\(p\)-Value)** & **(\(p\)-Value)** \\ \hline
1 & ARIMA(2,0,2) & \(5.27\times 10^{-5}\) & 0.449 & **0.7556** & \textless{}2.2 \(\times 10^{-16}\) & \textless{}2.2 \(\times 10^{-16}\) \\
2 & ARIMA(3,0,1) & 0.0008 & 0.257 & \(3.5\times 10^{-11}\) & **0.078** & \textless{}2.2 \(\times 10^{-16}\) \\
3 & ARIMA(2,0,1) & \(-\)0.0005 & 0.234 & \(1.594\times 10^{-11}\) & \(4.331\times 10^{-6}\) & \textless{}2.2 \(\times 10^{-16}\) \\
4 & ARIMA(2,0,2) & \(-\)0.0001 & 0.511 & \(0.00015\) & \textless{}5.70 \(\times 10^{-6}\) & \textless{}2.2 \(\times 10^{-16}\) \\
5 & ARIMA(2,0,2) & 0.0007 & 0.644 & **0.2001** & \textless{}3.201 \(\times 10^{-10}\) & \textless{}2.2 \(\times 10^{-16}\) \\
6 & ARIMA(1,0,1) & 0.0009 & 0.529 & \(5.668\times 10^{-9}\) & \(2.065\times 10^{-14}\) & \textless{}2.2 \(\times 10^{-16}\) \\
7 & ARIMA(2,0,1) & \(-\)0.0001 & 0.251 & \(5.951\times 10^{-8}\) & **0.093** & \textless{}2.2 \(\times 10^{-16}\) \\
8 & ARIMA(1,0,0) & \(-\)0.0002 & 0.518 & **0.1294** & \textless{}1.208 \(\times 10^{-8}\) & \textless{}2.2 \(\times 10^{-16}\) \\
9 & ARIMA(2,0,0) & 0.0003 & 0.678 & \(1.056\times 10^{-5}\) & \textless{}1.762 \(\times 10^{-8}\) & \textless{}2.2 \(\times 10^{-16}\) \\
10 & ARIMA(2,0,1) & \(3.99\times 10^{-5}\) & 0.235 & \(4.441\times 10^{-16}\) & \textless{}1.478 \(\times 10^{-7}\) & \textless{}2.2 \(\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Output of time series errors by section. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Type** & **Range** \\ \hline Status & Current traffic status of the section. & number & 0 to 4 \\ FromNorth & Starting Latitude (North). & number & 2099 to 2222 \\ FromWest & Starting Longitude (West). & number & 41,338 to 41,450 \\ ToNorth & Ending Latitude (North). & number & 2100 to 2223 \\ ToWest & Ending Longitude (West). & number & 41,338 to 41,449 \\ DailyHour & Measurement hour. & number & 0 to 23 \\ DailyMinute & Measurement minute. & number & 0 to 60 \\ Weekday & Weekday of the measurement. & number & 1 to 7 \\ DayMonth & Measurement day of the month. & number & 1 to 31 \\ Holiday & Boolean value representing the existence of a & holiday on that day. & Boolean & False or True \\ \hline Number of records: 24,533,298 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of the dataset for the XGBoost model.