# Analyzing and Forecasting Vessel Traffic Through the Panama Canal: A Comparative Study
## 3 Results  
The following Table 1 shows descriptive statistics of the monthly number of vessels transiting through the Panama Canal from January 2000 to December 2022.  
The results (Table 1) show that the mean and median values are 1154 and 1145 vessels, respectively, with a standard deviation of 99 vessels. The maximum monthly maritime transit recorded in recent years is 1431 vessels, while the minimum is 890 vessels. Additionally, the first quartile (Q\({}_{1}\) = 1082) and the third quartile (Q\({}_{3}\) = 1216) represent the 25 th and 75 th percentiles, respectively, and provide information about the central dispersion of the data. These quartiles indicate that 50% of the monthly observations of vessels transiting the Panama Canal fall between 1082 and 1216 vessels.  
The analysis of the historical data began with the decomposition of the original series to identify its behavior, including trend and seasonal patterns.  
The number of vessels transiting the Panama Canal from January 2000 to December 2022 is relatively stable (Figure 6) and reveals a seasonal pattern with a recurrent 12-month cycle, as shown in Figure 7. The results indicate that maritime traffic through the Panama Canal is significantly higher from January to April compared to other months.  
This set of visualizations provides a comprehensive view of fluctuations in frequency units, both monthly and annually, enabling a detailed analysis of the temporal dynamics of the series. The top panel displays the monthly evolution of the series across different calendar years (from January to December). Each line, distinguished by color, represents a full year and reveals recurring seasonal patterns as well as interannual variations in their magnitude and shape. The middle panel shows the temporal evolution disaggregated by month for the period from 2000 to 2022. In this case, each line and color correspond to a specific month, allowing for the analysis of behavior over time and facilitating the identification of month-specific trends and potential changes in seasonal patterns. Finally, the bottom panel presents boxplots summarizing the monthly distribution of the series values. This visualization clearly displays the median, interquartile range, dispersion, and presence of outliers, providing a concise and informative overview of the variability and  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Measure** & **Values** \\ \hline Mean & 1154 \\ Standard Deviation & 99 \\ Minimum & 890 \\ Maximum & 1431 \\ First Quartile & 1082 \\ Median & 1145 \\ Third Quartile & 1216 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive Statistics of Vessel Transit.  
relative stability of each month. In summary, the images presented in Figure 7 illustrate the behavior of irregularity by month and year. These results indicate that the series exhibits a strong component of high irregularity over time, with notable differences in the months of February and March, as well as in subsequent periods. From June onward, the series shows stability. Overall, the data do not display a pronounced trend (Figure 6).  
The following sections present the visualization and temporal analysis of the data series, enabling the exploration of behavior over time and the identification of possible patterns.  
Figure 6: Maritime transit through the Panama Canal, from 2000 to 2022.  
Figure 7: Decomposition of the time series into the trend, seasonal, and residual components.