# Analyzing and Forecasting Vessel Traffic Through the Panama Canal: A Comparative Study
## 4 Discussion and Conclusions  
This study proposed forecasting methods based on both classical statistical models, such as ARIMA and Holt-Winters, and modern machine learning techniques using neural networks, with the objective of estimating the vessel traffic through the Panama Canal and comparing their performance. As noted by [PERSON] et al. [51], reliable prediction of daily vessel traffic volume can support informed decision-making in operational management. Accordingly, various performance metrics were used to evaluate the robustness and accuracy of the forecasts [12; 44]. Figure 15: Comparison between Actual Observations and Forecasts of Vessel Traffic through the Panama Canal Using the Evaluated Models. In this study, three forecasting models were applied and compared as the following: the Seasonal Autoregressive Integrated Moving Average model (SARIMA), Holt-Winters exponential smoothing method, and Neural Network Autoregressive model (NNAR). The objective was to evaluate their performance in forecasting monthly vessel traffic through the Panama Canal, using standard evaluation metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results show that the NNAR model (RMSE = 83.96, MAE = 68.21, MAPE = 6.33%) and SARIMA model (RMSE = 87.58, MAE = 67.49, MAPE = 6.31%) achieved similar performance, whereas the Holt-Winters model exhibited considerably higher error values (RMSE = 106.17, MAE = 82.36, MAPE = 7.71%). Although SARIMA had slightly lower MAE and MAPE values, the NNAR model achieved the lowest RMSE, suggesting a better ability to capture the complexity of nonlinear patterns, as well as the seasonality present in the series. To determine whether these differences were statistically significant, the Diebold-Mariano test was applied. The results indicated statistically significant differences between the SARIMA and Holt-Winters models (DM = 2.61, \(p\) = 0.012), as well as between the Holt-Winters and NNAR models (DM = 5.31, \(p\) = 0.0001). In contrast, no significant differences were found between the NNAR and SARIMA models (DM = \(-0.07,p\) = 0.944), confirming that both offer comparable predictive accuracy. These findings demonstrate that the neural network model achieved superior predictive performance compared to the SARIMA model in terms of error, thereby extending the empirical evidence reported by [PERSON] et al. [16] in predicting container ship traffic at Rajaee Port; by [PERSON]. [52], who utilized neural networks to estimate marine traffic flow; and by [PERSON] et al. [53], who applied deep learning approaches for vessel flow forecasting. Additionally, a recent study combined an autoregressive time series model with a data assimilation method to predict the number of vessels transiting the Panama Canal, using data collected between 1 March and 31 March 2021 [26]. Although this analysis did not consider a long-term historical series, it represents the study most similar to ours identified in the literature. Recent studies have employed machine learning techniques for forecasting in the maritime sector. [PERSON] et al. [54] applied a variety of statistical, machine learning, and deep learning approaches for predictive analysis of port operations, with a specific focus on modeling vessel Total Stay Time and Delay Time. Similarly, [PERSON] et al. [55] developed a hybrid machine learning-based approach for the accurate estimation of vessels' estimated time of arrival at seaports. The combination of traditional statistical techniques with advanced deep learning approaches has led to significant advances in maritime traffic forecasting. These models provide valuable tools to support decision-making in port management and maritime transport planning. The findings of this study on the temporal dynamics of vessel traffic through the Panama Canal are particularly relevant for the various stakeholders involved in maritime transport operations.