# Prediction of Traffic Volume Based on Deep Learning Model for AADT Correction
## 4 Statistical Learning Verification and Machine Learning Model Analysis and Evaluation
### Machine Learning Model Analysis and Evaluation  
(1) SARIMA Model Analysis Results  
In evaluating the SARIMA model, the analysis of sample errors revealed no discernible patterns in the residuals between the estimated and actual values, suggesting the absence of significant heterogeneity issues; therefore, no additional log transformations were necessary. The Ljung-Box (LB) test was conducted to verify the accuracy of the model judgments. The LB test yielded a significance probability of 0.04, which is below the threshold of 0.1, indicating minimal autocorrelation. Consequently, the optimal parameters for the SARIMA model were determined through the auto grid searching method without the need for further log transformations or differencing. The selection of optimal parameters was guided by [PERSON]'s information criterion (AIC), the Bayesian information criterion (BIC), and various significance tests. The results are summarized in Table 2.  
The overall prediction results indicated excellent performance, averaging approximately 85%; however, there was a notable decline in the prediction accuracy due to long-term missing data from 2019, which adversely affected the model's ability to reflect the periodicity and trends accurately. Table 3 presents the evaluation results of the SARIMA (4,1,3)(4,0,3) 12 model, revealing the discrepancy between the actual and predicted values, which ranged from a minimum of 3.28% to a maximum of 14.59%. Although the SARIMA model typically uses MAPE to estimate prediction errors, for consistency in comparisons \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Model: SARIMA (4,1,3)(4,0,3) 12**} \\ \hline
**Type** & **Factor** & **SE Factor** & \(\boldsymbol{p>|z|}\) \\ \hline Autoregressive (AR) (time lag 1) & \(-1.1503\) & 0.041 & 0.000 \\ \hline AR (time lag 2) & \(-0.1593\) & 0.051 & 0.002 \\ \hline AR (time lag 3) & 0.0759 & 0.061 & 0.210 \\ \hline AR (time lag 4) & \(-0.2939\) & 0.040 & 0.000 \\ \hline Moving average (MA) (time lag 1) & 0.7886 & 0.035 & 0.000 \\ \hline MA (time lag 1) & \(-0.6714\) & 0.034 & 0.000 \\ \hline MA (time lag 1) & \(-0.7927\) & 0.034 & 0.000 \\ \hline AR season (time lag 1) & 0.2791 & 0.309 & 0.367 \\ \hline AR season (time lag 2) & 0.0555 & 0.353 & 0.875 \\ \hline AR season (time lag 3) & \(-0.7049\) & 0.296 & 0.017 \\ \hline AR season (time lag 4) & \(-0.1349\) & 0.049 & 0.006 \\ \hline MA season (time lag 1) & \(-0.3960\) & 0.307 & 0.197 \\ \hline MA season (time lag 1) & \(-0.0459\) & 0.372 & 0.902 \\ \hline MA season (time lag 1) & \(-0.7397\) & 0.316 & 0.019 \\ \hline AIC & 6983 & Ljung–Box (Q) & 0.04 \\ \hline BIC & 7068 & Log-likelihood & \(-3201\) \\ \hline \hline \end{tabular} Source: traffic volume correction and prediction using the SARIMA algorithm, 2021.  
\end{table} 
Table 2: Optimal parameter estimation results for the SARIMA model. across the statistical, machine learning, and deep learning models, MAPE was converted to MAE. The converted MAE was analyzed to be 0.158. 2. Prophet Model Analysis A separate analysis was conducted using the min-max scaling method to standardize the range of data values. Evaluation metrics included RMSE, MAE, and R\({}^{2}\). The analysis focused on two specific points, as detailed in Table 4. Given its nature as a univariate regression model, R\({}^{2}\), which indicates the linear fit, serves as a measure of prediction accuracy. Figure 4 depicts the results of predicting the hourly traffic volume at point 10001 using the Prophet model, where MAE is 0.117, RMSE is 0.147, and R\({}^{2}\) is 0.914, indicating considerably high predictive performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point** & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline
10001 & 0.117 & 0.147 & 0.914 \\ \hline
10004 & 111.687 & 158.050 & 0.847 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation results of the Prophet model. Figure 4: Prophet model’s prediction results (point 10001).