A comparative evaluation of machine learning approaches for container freight rates prediction

Kim, Namhun; Cha, Junhee; Jeon, Junwoo Article A comparative evaluation of machine learning approaches for container freight rates prediction Asian Journal of Shipping and Logistics (AJSL) Provided in Cooperation with: Korean Association of Shipping and Logistics, Seoul Suggested Citation: Kim, Namhun; Cha, Junhee; Jeon, Junwoo (2025) : A comparative evaluation of machine learning approaches for container freight rates prediction, Asian Journal of Shipping and Logistics (AJSL), ISSN 2352-4871, Elsevier, Amsterdam, Vol. 41, Iss. 2, pp. 99-109, https://doi.org/10.1016/j.ajsl.2025.05.001 This Version is available at: https://hdl.handle.net/10419/329761 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ A comparative evaluation of machine learning approaches for container freight rates prediction Namhun Kim a , Junhee Cha a , Junwoo Jeon b,* a Department of Business Administration, Sungkyul University, Republic of Korea b Department of Global Logistics, Sungkyul University, Republic of Korea ARTICLE INFO Keywords: Container Freight Rates Machine learning Decision Tree Random Forest LSTM Prophet ABSTRACT This study evaluates the predictive performance of four models—Decision Tree, Random Forest, Prophet, and LSTM—in forecasting container freight rates, a key metric for strategic decision-making in the shipping industry. To address data heterogeneity, Min-Max normalization was applied, and the Johansen co-integration test confirmed long-term relationships among the variables, justifying the use of raw data in our analysis. Performance was assessed using MSE, RMSE, NMSE, MAE, MAPE and SMAPE. While both Decision Tree and Random Forest models yielded lower absolute errors compared to LSTM and Prophet, the Decision Tree model demonstrated superior relative accuracy, outperforming Random Forest by approximately 91.8 % on the USWC route, 52.1 % on USEC, 43.5 % on MED, and 22.7 % on NEUR. These findings highlight the robustness of the Decision Tree model for container freight rate forecasting under volatile market conditions. 1. Introduction The shipping industry is a cornerstone of global trade, responsible for transporting over 80 % of the world’s cargo. This vital function underpins global economic growth and supply chain stability (Wang et al., 2024). In this context, the accurate prediction of ocean freight rates is critical. Freight rates not only reflect current market conditions but also serve as a mechanism for balancing supply and demand through strategic rate adjustments (Jeon et al., 2020; Scarsi, 2007; Schramm & Munim, 2021; Wang et al., 2024). The importance of forecasting ocean freight rates is multifaceted. First, key stakeholders—including ship owners, cargo carriers, logistics companies, and end consumers—rely on these predictions for informed decision-making across various functions such as product pricing, cost accounting, financial management, and asset allocation (Hirata & Matsuda, 2022; Jeon et al., 2021). The volatility of freight rates is a fundamental component of maritime transport costs; therefore, precise forecasting of this volatility is crucial for market participants (Naima et al., 2023). Second, the inherent periodicity of ocean freight rates arises from the lengthy interval between ship orders and deliveries, which typically exceeds two years. This temporal lag reinforces cyclical patterns in freight rate dynamics (Scarsi, 2007). Third, ship owners make routine decisions regarding ship sales and charters based on prevailing freight rate levels, further emphasizing the need for robust forecasting (Jeon et al., 2020). Fourth, for shippers, accurate rate predictions are essential as logistics costs are directly correlated with freight rates—costs tend to escalate during periods of high rates and decline when rates are low. Additionally, seasonal variations, exemplified by the implementation of Peak Season Surcharges (PSS) in months such as March or October, further complicate the forecasting landscape (Yin & Shi, 2018). Finally, external shocks, including geopolitical risks and events such as the Suez Canal blockage during the COVID-19 pandemic and the recent Red Sea crisis, have demonstrated significant adverse impacts on container freight rates. Incorporating these disruptions into forecasting models has been shown to enhance predictive accuracy (Naima et al., 2023). Moreover, the shipping industry is notably capital-intensive, with substantial financial commitments required for ship ordering and operation (Jeon & Yeo, 2017). Overcapacity, often resulting from aggressive shipbuilding, can precipitate a decline in freight rates, thereby intensifying the need for accurate market assessments and risk evaluations. For instance, using system dynamics, Jeon et al. (2020) identified a cyclical pattern of approximately 32 months in the China Container Freight Index (CCFI), highlighting the interplay between supply-demand imbalances. Additionally, stringent environmental regulations imposed by the International Maritime Organization (IMO), * Corresponding author. E-mail address: [email protected] (J. Jeon). Contents lists available at ScienceDirect The Asian Journal of Shipping and Logistics journal homepage: www.elsevier.com/locate/ajsl https://doi.org/10.1016/j.ajsl.2025.05.001 Received 21 March 2025; Accepted 6 May 2025 The Asian Journal of Shipping and Logistics 41 (2025) 99–109 Available online 17 May 2025 2092-5212/© 2025 The Author(s). Published by Elsevier B.V. on behalf of The Korean Association of Shipping and Logistics, Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). such as the Energy Efficiency Design Index (EEDI), Energy Efficiency Ship Index (EEXI), and Carbon Intensity Indicator (CII), are compelling shipping companies to invest in eco-friendly vessels. These regulatory requirements further amplify the necessity for reliable freight rate forecasts to mitigate the risks associated with new ship orders (Bayraktar & Yuksel, 2023; Lee, 2024). In light of these considerations, this study aims to compare the predictive performance of four distinct models—Prophet, Decision Tree, Random Forest, and LSTM—in forecasting container freight rates. The objective is to identify the model that most effectively captures the complex dynamics of ocean freight rates, thereby supporting more informed decision-making by industry stakeholders. The remainder of this paper is organized as follows. Chapter 2 reviews relevant literature on container freight rate prediction and discusses prior applications of the Prophet, Decision Tree, Random Forest, and LSTM models. Chapter 3 details the data and methodological framework employed. Chapter 4 presents empirical findings and provides a comparative evaluation of the models. Chapter 5 discusses the implications of the findings, and Chapter 6 concludes the study. 2. Literature review 2.1. Forecasting studies on container freight rates Container freight rates are critical indicators for a multitude of stakeholders within the shipping industry, influencing decisions ranging from pricing and financial management to asset allocation. Traditionally, econometric models—such as ARIMA, VAR, VEC, and ARMA—have been extensively employed to forecast these rates (Koyuncu & Tavacıo˘ glu, 2021; Munim & Schramm, 2017). For example, Schramm and Munim (2021) conducted comparative analyses between ARIMA and VAR, while Munim and Schramm (2021) extended this comparison to ARIMA and VEC. In another study, Chen et al. (2021) proposed an innovative hybrid approach by integrating empirical mode decomposition (EMD) with ARMA. Luo et al. (2009) further advanced the field by employing supply and demand dynamics for forecasting container freight rates. Notwithstanding these contributions, the inherently non-linear and complex nature of container freight rate data presents substantial challenges for traditional econometric models (Hirata & Matsuda, 2022). This limitation has catalyzed a shift towards the adoption of machine learning and deep learning techniques, which are more adept at capturing non-linear patterns. Recent studies have demonstrated that deep learning models, such as LSTM, can outperform conventional approaches in certain contexts; for instance, Hirata and Matsuda (2022) reported superior predictive performance of LSTM over ARIMA for deep-sea routes, although results were comparable for short-sea routes. Moreover, Chen et al. (2024) showed that a CNN-LSTM hybrid model could achieve an R² exceeding 90 %, outperforming an ARIMA-SVR framework. Similarly, machine learning models such as Random Forest have been shown to deliver prediction accuracy above 80 % (Feng, 2022; Khan & Hussain, 2022). Complementary work by Jeon et al. (2021) compared ARIMA, VEC, and System Dynamics models, finding that the latter reduced prediction error by approximately 30 % on average, thereby offering distinct advantages in capturing market dynamics. 2.2. Studies on specific forecasting models In addition to broad econometric approaches, various forecasting models have been applied across different domains. Their relevance to container freight rate prediction is elucidated below. 2.2.1. Decision tree models Decision tree methodologies have proven effective in numerous forecasting applications. Liu et al. (2017a) applied decision trees for copper price prediction, achieving robust performance as measured by MAPE and RMSE. Bala (2010) extended this application to demand forecasting for Indian retailers, demonstrating that decision tree-based models outperformed other methods—such as ARIMA and SARIMA—- over both short and long-term horizons. Hybrid models that combine decision trees with artificial neural networks (ANN) have further enhanced prediction accuracy (Chang, 2011; Tsai & Wang, 2009), reinforcing the versatility of decision tree frameworks. 2.2.2. Random forest models Random Forest, an ensemble extension of decision trees, mitigates the risk of overfitting and enhances predictive stability. Liu and Li (2017b) utilized Random Forest to forecast gold price fluctuations, identifying critical predictors such as the DJIA and S&P 500 indices. Kumar and Thenmozhi (2006), demonstrated that Random Forest provided competitive accuracy relative to SVM, LDA, and logistic regression for predicting stock volatility. Subsequent studies by Abraham et al. (2022) and Vairagade et al. (2019) have consistently reported that Random Forest outperforms alternative methods in various forecasting contexts. Huertas Tato and Centeno Brito (2018), further validated these findings through applications in solar energy production forecasting, while Xue et al. (2021) compared multi-objective Random Forest variants, confirming its robustness in handling complex prediction tasks. 2.2.3. LSTM models Long Short-Term Memory (LSTM) networks, a subset of recurrent neural networks (RNN), are particularly well-suited for time-series forecasting due to their ability to capture long-term dependencies. Bhandari et al. (2022) found that single-layer LSTM models provided superior predictive accuracy for S&P 500 closing prices when evaluated against RMSE, MAPE, and R² metrics. Conversely, Abbasimehr et al. (2020) reported that multi-layer LSTM models achieved even greater performance, outperforming conventional models such as ARIMA, ANN, and SVM. Sagheer and Kotb (2019) extended the LSTM architecture (DLSTM) for petroleum production forecasting, demonstrating notable improvements in RMSE and MAPE, while Siami-Namini et al. (2018) documented significant error reductions of 84–87 % in comparison to ARIMA models. 2.2.4. Prophet models Prophet, developed by Taylor and Letham (2018), is designed for robust time-series forecasting by accommodating trends, seasonality, and external events. Empirical comparisons by Jha and Pande (2021) revealed that Prophet achieved lower RMSE and MAPE values compared to ARIMA in the context of supermarket sales forecasting. Similarly, Yenido˘ gan et al. (2018) applied both models to Bitcoin price prediction, reporting an R² of 0.94 for Prophet versus 0.68 for ARIMA. Kaninde et al. (2022) further demonstrated the utility of Prophet in volatile stock market forecasting, particularly due to its ability to integrate holiday effects and other exogenous factors. Recent external shocks, including the Suez Canal blockage during COVID-19 and the Red Sea crisis, underscore the importance of incorporating exogenous variables into forecasting models to enhance predictive accuracy (Naima et al., 2023; Wang et al., 2024). 2.2.5. Contributions Despite the extensive body of work utilizing econometric models for container freight rate prediction, there remains a significant gap in the application of advanced machine learning and deep learning techniques to this domain. In particular, the relative underutilization of models such as Prophet, Random Forest, and LSTM—compared to traditional approaches—suggests a promising avenue for further research. Additionally, decision tree-based models have received limited attention in the context of container freight rate forecasting, despite demonstrated success in other fields. Therefore, the present study seeks to address these gaps by systematically comparing the performance of Prophet, N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 100 Decision Tree, Random Forest, and LSTM models. This comparative analysis aims to elucidate the strengths and limitations of each approach and to identify the most effective methodology for capturing the complex, non-linear dynamics inherent in container freight rate data. 3. Methodology 3.1. Data Ocean freight rates are influenced by various factors, including supply and demand dynamics, cargo weight and volume, and the distance to destination (Khan & Hussain, 2022). Recent geopolitical developments—such as the Red Sea crisis, which prompted container ships to bypass the Suez Canal in favor of the South African Cape of Good Hope—have further impacted these rates. Historical events, including the global financial crisis, the COVID-19 pandemic, and episodes of overcapacity, have also demonstrated significant effects on ocean freight rates (Naima et al., 2023; Wang et al., 2024). To capture these dynamics, this study utilizes variables representing container shipping volume, container capacity, and key economic indicators. Specifically, Asia-Europe capacity and Asia-North America capacity are employed to quantify shipping capacity, while Asia-Europe shipping volume and Asia-North America shipping volume measure shipping volume. Ocean freight rates are examined along the North American, European, and Mediterranean Sea routes, as derived from the Shanghai Containerized Freight Index (SCFI). The economic indicators incorporated into the analysis include Global Economic Policy Uncertainty (EPU), the G20 Composite Leading Indicator (CLI), and Global Geopolitical Risk (GPR). EPU is calculated based on the frequency of terms such as "economy" and "policy" in media articles (Baker et al., 2016), CLI reflects expectations of future economic activity (OECD), and GPR quantifies geopolitical tensions based on news frequency (Caldara & Iacoviello, 2022). This study utilizes monthly data spanning from January 2014 to June 2024. Due to the heterogeneous units of measurement (e.g., TEU versus USD/TEU), all features are normalized using a Min-Max scaling technique, which scales values to the [0,1] range. Subsequently, the Johansen co-integration test is performed to ascertain the existence of long-term relationships among the variables. The presence of cointegration justifies the use of the raw data in the forecasting models. Table 1 provides a summary of the descriptive statistics for the data used in this study. 3.2. Forecasting models 3.2.1. Prophet model The Prophet model, introduced by Taylor and Letham (2018), is specifically designed for robust time-series forecasting. Its principal strength lies in its capacity to model seasonal patterns, long-term trends, and holiday effects independently, allowing for easy customization to specific business contexts. This flexibility enables Prophet to effectively capture the non-linear characteristics and periodic fluctuations inherent in ocean freight rate data. 3.2.2. Decision tree and random forest models The Decision Tree model is a well-established method in predictive analytics, originally conceptualized by Belson (1959) and further developed through the CART methodology by Breiman et al. (1986). Although decision trees are intuitive and easy to interpret, they are susceptible to overfitting. To address this limitation, Random Forest—an ensemble learning technique proposed by Breiman (2001)—aggregates the predictions of multiple decision trees through a voting mechanism. This ensemble approach mitigates overfitting and enhances the model’s performance, particularly when dealing with high-dimensional data. 3.2.3. LSTM model Long Short-Term Memory (LSTM) networks, introduced by Hochreiter (1997), are a specialized type of recurrent neural network designed to overcome the limitations of traditional RNNs in capturing long-term dependencies. LSTM networks incorporate gating mechanisms—namely, the input, forget, and output gates—along with a memory cell that preserves and updates information as needed. These features address the vanishing gradient problem, thereby enabling the efficient learning of temporal dependencies and making LSTM particularly well-suited for time-series forecasting tasks such as predicting ocean freight rates. 3.2.4. Model settings Random Search was employed to identify the optimal hyperparameter configurations for the Decision Tree, Random Forest, and Prophet models. In contrast, the LSTM model was trained using a consistent hyperparameter configuration across all sections, a design choice made to balance performance and computational demands. Table 2 presents the section-specific settings used for hyperparameter optimization. 3.2.5. Model validation To assess the forecasting performance of the models, this study employs a comprehensive set of evaluation metrics: Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Normalized Mean Squared Error (NMSE) and Symmetric Mean Absolute Percentage Error (SMAPE). MAE provides a direct measure of the average absolute error between the predicted and actual values. MAPE expresses this error as a Table 1 Data descriptive statistics. Count Mean Std Min Max 50 % EPU* 126 208.86 72.57 86.63 431.73 208.31 GPR* * 126 105.78 33.75 58.42 318.95 102.19 CLI* ** 126 99.73 1.45 89.48 101.41 99.99 Capacity_EUR* ** * 126 1858,579 153,128.7 1559,476 2142,365 1860,088 Capacity_NA* ** * 126 2015,801 424,777.4 1462,072 2912,504 1876,666 Volume_EUR* ** * 126 1330,787 153,564.1 67,620 1616,700 1364,350 Volume_NA* ** * 126 1615,153 284,394.8 81,270 2119,400 1582,550 Med* ** ** 126 2019.58 2064.47 220.50 7522.75 984.71 NEUR* ** ** 126 1847.21 2055.13 223.50 7784.25 912.63 USWC* ** ** 126 2587.77 1895.83 796.50 8079.00 1800.13 USEC* ** ** 126 4091.98 2631.86 1589.50 2962.75 11,778.50 * Baker, S. R., Bloom, N., & Davis, S. J. (2016). "Measuring Economic Policy Uncertainty." Available at: Policy Uncertainty. / Unitless Index * * Caldara, D and Iacoviello, M. (2022). "Global Policy Uncertainty." Available at: Matteo Iacoviello’s Website. / Unitless Index * **OECD. "Composite Leading Indicator (CLI) - G20." Available at: OECD. / Unit: Long-term average =100 * ** *Bloomberg L.P. "Shipping Capacity and Shipping Volume Data." Bloomberg Terminal. / Unit: TEU * ** **Shanghai Shipping Exchange. "Shanghai Containerized Freight Index." Available at: Shanghai Shipping Exchange. / Unit: USD/TEU, Unit: USD/FEU N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 101 percentage, facilitating comparisons across models with different scales. MSE and RMSE, by emphasizing larger errors through squaring, offer insights into the models’ sensitivity to significant deviations. NMSE normalizes the error relative to the variance of the data, allowing for a relative assessment of predictive performance. MAPE has a problem that the error rises infinitely when the actual value is close to 0, and SMAPE is used to compensate for this. SMAPE reflects the symmetry between the predicted and actual values and works stably near zero. Lower values across these metrics indicate better model performance, guiding the selection of the most effective forecasting approach for container freight rates. 4. Results 4.1. Johansen test The Johansen co-integration test was conducted to ascertain the existence of a long-term equilibrium relationship among the variables. In this test, the null hypothesis posits that the number of co-integrating vectors is less than a specified rank (n <r), whereas the alternative hypothesis asserts that r is less than or equal to n. If the test statistic exceeds the critical value, the null hypothesis is not rejected; conversely, it is rejected when the test statistic falls below the critical value. As summarized in Table 3, the test results confirm the presence of cointegration across all routes examined. Consequently, despite any nonstationarity in the individual series, the existence of a long-term relationship justifies the application of the raw data in subsequent modeling. Specifically, the number of co-integrations was determined to lie within range 2 <r ≤3 for both the USEC and USWC routes, and within 1 <r ≤2 for the MED and NEUR routes. 4.2. Model setting All models utilizing normalized data were trained using 80 % of the dataset, with the remaining 20 % reserved for testing. The performance evaluations presented in Table 5 are based on models trained using the hyperparameter configurations detailed in Table 4. Specifically, Table 4 Table 2 Section settings for hyperparameter optimization. Decision Tree Random Forest Prophet LSTM Max Depth: 1–20 N Estimators: 1–100 Max Depth: 1–20 Min Samples Split: 10–100 Min Samples Leaf: 1–20 Max Features: 1–15 Max Leaf Nodes: 1–100 Min Weight Fraction Leaf: 0–1 Growth: Linear, Logistic Daily Seasonality: True, False Weekly Seasonality: True, False Yearly Seasonality: True, False Changepoint Prior Scale: 0.001–100(Log Scale) Seasonality Prior Scale: 0.001–100(Log Scale) Sequence Length: 3 Dropout: 0.5 Units: 128 Epochs: 100 Batch Size: 64 Optimizer: Adam Learning Rate: 0.001 Loss: MSE Min Samples Split: 10–100 Min Samples Leaf: 1–20 Max Features: 1–15 Max Leaf Nodes: 1–100 Min Weight Fraction Leaf: 0–1 Criterion: squared_error, friedman_mse, absolute_error, poisson Table 3 Johansen test. Route r_0 r_1 Test Statistic Critical Value (%) USEC 0 6 125.2 95.75 1 6 84.97 69.82 2 6 51.54 47.85 3 6 28.44 29.80 USWC 0 6 134.0 95.75 1 6 87.06 69.82 2 6 53.06 47.85 3 6 27.28 29.80 MED 0 6 125.5 95.75 1 6 75.16 69.82 2 6 44.02 47.85 NEUR 0 6 129.0 95.75 1 6 76.92 69.85 2 6 45.93 47.85 Table 4 Settings of hyperparameter. Route Model Hyperparameter USWC Decision Tree random_state=42, criterion=’squared_error’, max_depth=19, max_features=2, max_leaf_nodes=68, min_samples_leaf=15, min_samples_split=2, min_weight_fraction_leaf=0 Random Forest random_state=42, max_depth=6, max_features=7, max_leaf_nodes=81, min_samples_leaf=1, min_samples_split=16, min_weight_fraction_leaf=0, n_estimators=21, bootstrap=True, oob_score=False, n_jobs=None LSTM Sequence Length=3, Dropout=0.5, Units=128, Epochs=100, Batch Size=64, Optimizer=Adam, Learning Rate=0.001, Loss=MSE Prophet growth=’logistic’, changepoint_prior_scale=0.0081, seasonality_prior_scale=572.237, yearly_seasonality=True, daily_seasonality=False, weekly_seasonality=False USEC Decision Tree random_state=42, criterion=’squared_error’, max_depth=15, max_features=13, max_leaf_nodes=27, min_samples_leaf=13, min_samples_split=52, min_weight_fraction_leaf=0 Random Forest random_state=42, max_depth=6, max_features=3, max_leaf_nodes=96, min_samples_leaf=11, min_samples_split=21, min_weight_fraction_leaf=0, n_estimators=26, bootstrap=True, oob_score=False, n_jobs=None LSTM Sequence Length=3, Dropout=0.5, Units=128, Epochs=100, Batch Size=64, Optimizer=Adam, Learning Rate=0.001, Loss=MSE Prophet growth=’logistic’, changepoint_prior_scale=0.0035, seasonality_prior_scale=0.0013, yearly_seasonality=True, daily_seasonality=False, weekly_seasonality=False MED Decision Tree random_state=42, criterion=’squared_error’, max_depth=19, max_features=9, max_leaf_nodes=74, min_samples_leaf=6, min_samples_split=16, min_weight_fraction_leaf=0 Random Forest random_state=42, max_depth=7, max_features=14, max_leaf_nodes=38, min_samples_leaf=10, min_samples_split=18, min_weight_fraction_leaf=0, n_estimators=39, bootstrap=True, oob_score=False, n_jobs=None LSTM Sequence Length=3, Dropout=0.5, Units=128, Epochs=100, Batch Size=64, Optimizer=Adam, Learning Rate=0.001, Loss=MSE Prophet growth=’logistic’, changepoint_prior_scale=0.0081, seasonality_prior_scale=0.6136, yearly_seasonality=True, daily_seasonality=False, weekly_seasonality=False NEUR Decision Tree random_state=42, criterion=’squared_error’, max_depth=19, max_features=3, max_leaf_nodes=70, min_samples_leaf=3, min_samples_split=27, min_weight_fraction_leaf=0 Random Forest random_state=42, max_depth=13, max_features=12, max_leaf_nodes=76, min_samples_leaf=2, min_samples_split=40, min_weight_fraction_leaf=0, n_estimators=57, bootstrap=True, oob_score=False, n_jobs=None LSTM Sequence Length=3, Dropout=0.5, Units=128, Epochs=100, Batch Size=64, Optimizer=Adam, Learning Rate=0.001, Loss=MSE Prophet growth=’logistic’, changepoint_prior_scale=0.0023, seasonality_prior_scale=0.0327, yearly_seasonality=True, daily_seasonality=False, weekly_seasonality=False N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 102 outlines the optimized hyperparameter settings for each of the four models, while Table 5 compares the predictive performance of these models following training with the specified configurations. 4.3. Model comparison The predictive performance of the four forecasting models—Decision Tree, Random Forest, LSTM, and Prophet—was rigorously evaluated using six metrics: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Normalized Mean Squared Error (NMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Symmetric Mean Absolute Percentage Error (SMAPE). Table 5 presents a detailed summary of these evaluation indicators for each shipping route. Overall, the Decision Tree and Random Forest models demonstrated superior performance compared to the LSTM and Prophet models when assessed using absolute error metrics (MSE, RMSE, NMSE, and MAE). This observation suggests that tree-based methods are more effective in capturing the underlying non-linear dynamics of container freight rate data. The lower error values achieved by these models indicate their enhanced capability to model the complex relationships present in the dataset. For the USWC route, the Random Forest model achieved the lowest absolute error values, recording an MSE of 0.0322, an RMSE of 0.1796, an NMSE of 0.5853, and an MAE of 0.1007. Specifically, the MSE obtained by the Random Forest model was approximately 58.6 % lower than that of the Decision Tree, 85.2 % lower than that of the Prophet model, and 99.15 % lower than that of the LSTM model. These improvements in error metrics underscore the robust performance of the Random Forest approach in capturing the dynamics of the USWC route. In contrast, for the USEC route, the Decision Tree model exhibited the most favorable performance. The Decision Tree recorded an MSE of 0.0310, an NMSE of 0.4559, an RMSE of 0.1579, and an MAE of 0.1007, outperforming the Random Forest model by a modest margin. Specifically, its MSE was about 2.9 % lower than that of the Random Forest, approximately 87.2 % lower than that of the Prophet model, and nearly 99.2 % lower than that of the LSTM model. This result indicates that, for the USEC route, the Decision Tree model more effectively captures the underlying data structure. For the MED route, while the Random Forest model generally achieved lower error metrics—with an MSE of 0.0347, an RMSE of 0.1863, and an NMSE of 0.4359—the Decision Tree model yielded the lowest MAE at 0.1181. The performance differences between these models, although small, suggest that each model may have strengths in capturing different aspects of the data variability for the MED route. On the NEUR route, the Random Forest model again recorded the lowest absolute error values, with an MSE of 0.0447, an RMSE of 0.2115, an NMSE of 0.5434, and an MAE of 0.1297. The Random Forest’s performance on this route was approximately 29.3 % better in terms of MSE, 15.9 % better in RMSE, and 30.5 % better in NMSE compared to the Decision Tree model. Nonetheless, the differences in performance metrics between the two models on the NEUR route were relatively marginal. A comparison between MAPE and SMAPE reveals that SMAPE consistently demonstrates better performance across all routes. This suggests that many of the actual values used in the MAPE denominator are close to zero, thereby inflating the MAPE error. To address this issue, both MAPE and SMAPE were jointly examined, and models exhibiting relatively stable values across both metrics were selected. Based on this comprehensive evaluation, the Decision Tree and Random Forest models generally outperformed the LSTM and Prophet models across most routes. Despite the favorable outcomes for both the Decision Tree and Random Forest models with respect to absolute error metrics, the relative error measure—MAPE and SMAPE—revealed considerably higher prediction error ratios across all models. This elevated MAPE and SMAPE is largely attributable to the increased volatility in container freight rates following disruptions such as the COVID-19 pandemic and the Red Sea crisis. Elevated MAPE and SMAPE values across all models are largely attributable to the increased volatility in container freight rates following disruptions such as the onset of the COVID-19 pandemic and the Red Sea crisis, which amplified global supply chain disturbances and resulted in larger percentage errors, as illustrated in Fig. 1. Comparing SMAPE, it was analyzed that USEC and MED have good decision tree performance, and USWC and NEUR have good Random Forest performance. Notably, a comparison of the MAPE values across the routes indicates that the Decision Tree model consistently exhibits lower relative error ratios than the Random Forest model. Specifically, the Decision Tree model achieved MAPE improvements of approximately 91.8 % for the USWC route, 52.1 % for the USEC route, 43.5 % for the MED route, and 22.7 % for the NEUR route when compared to the Random Forest model. Therefore, both MAPE and SMAPE adopted a relatively stable Decision Tree. Finally, using the Decision Tree model, the influence of various features on container freight rates was visualized across all routes. SHAP (SHapley Additive Explanations) was employed to quantitatively assess the impact of these features on the machine learning prediction outcomes. The graphical representations of feature influence for the Random Forest, Prophet, and LSTM model predictions are provided in the Appendix. Specifically, both the Decision Tree and Random Forest models utilized SHAP for feature impact visualization, the Prophet model evaluated feature influence through regression coefficients, and the LSTM model illustrated influence based on the average weights of its feature set. 5. Discussion The empirical analysis presented in Figs. 2–5elucidates the multifaceted determinants of container freight rates, emphasizing the critical roles of both supply-side and demand-side factors. In particular, capacity and volume exert substantial influences on freight rate fluctuations across all examined routes. These findings reinforce the theoretical framework advanced in earlier studies (Jeon et al., 2020; Scarsi, 2007), which posit that shipping capacity and shipping volume are primary drivers of freight rate dynamics. Beyond these fundamental supply-demand variables, our analysis highlights the pivotal role of the G20 CLI on routes other than USEC. As a Table 5 Evaluation indicators of models. Route indicator Decision Tree Random Forest LSTM Prophet USWC MSE 0.0778 0.0322 3788.1917 0.2171 RMSE 0.2790 0.1796 61.5482 0.4659 NMSE 0.8638 0.5853 75024.7661 1.7127 MAE 0.1615 0.1007 54.7361 0.4194 MAPE 36.9699 448.6831 39944.7295 330.4461 SMAPE 50.0792 47.3774 83.4179 73.5523 USEC MSE 0.0249 0.0310 3873.1899 0.2420 RMSE 0.1579 0.1761 62.2349 0.4920 NMSE 0.3618 0.4559 56941.6229 2.3690 MAE 0.1007 0.1146 55.1988 0.4235 MAPE 53.8369 112.3587 87888.3997 365.6392 SMAPE 42.1499 55.9611 76.8371 88.9091 MED MSE 0.0427 0.0347 4025.4914 0.1472 RMSE 0.2068 0.1863 63.4467 0.3837 NMSE 0.5136 0.4359 136494.9406 1.6701 MAE 0.1181 0.1265 56.1486 0.3487 MAPE 45.8080 81.1313 23215.9150 152.6911 SMAPE 43.2302 55.3836 41.5510 71.0931 NEUR MSE 0.0632 0.0447 3363.9074 0.1842 RMSE 0.2514 0.2115 57.9992 0.4292 NMSE 0.9562 0.5434 40844.9406 1.9608 MAE 0.1559 0.1297 52.3133 0.3877 MAPE 81.4221 105.2359 38170.2764 342.0722 SMAPE 66.1932 60.7961 68.7988 93.0079 N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 103 comprehensive measure that encapsulates key facets of economic activity—such as manufacturing performance, consumer confidence, and new order levels—the CLI serves as a robust proxy for assessing the overall economic environment. High CLI values typically signal an expanding economy, prompting shipping companies to increase capacity in anticipation of rising demand. Conversely, low CLI readings suggest economic stagnation or contraction, thereby incentivizing strategies such as capacity reduction or blank sailing. The strong correlation observed between CLI fluctuations and freight rate movements underscores its utility as a leading indicator for maritime transport planning. The analysis also reveals that EPU significantly impacts container freight rates on most routes, with the notable exception of the NEUR route. In recent years, ongoing tariff disputes and anti-dumping investigations—particularly between Europe and the United States Fig. 1. SCFI. Fig. 2. The influence of feature (USWC). Fig. 3. The influence of feature (USEC). Fig. 4. The influence of feature (MED). Fig. 5. The influence of feature (NEUR). N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 104 concerning imports from China—have elevated EPU levels. These conditions have led shippers to increase import volumes preemptively, which, in turn, have driven shipping companies to expedite the implementation of Peak Season Surcharges (PSS). A case in point is Maersk’s decision to enforce PSS earlier than usual for shipments from the Asia Pacific region to North America and Canada, a response attributed to surging import volumes observed in early July 2024. The muted influence of EPU on the NEUR route is likely due to the stabilizing effect of the European Union’s integrated economic framework, which buffers against policy-induced volatility. Furthermore, the GPR indicator has demonstrated a pronounced impact on the MED and NEUR routes. The recent Red Sea crisis, characterized by the occupation of the Red Sea by Yemeni Houthi rebels starting in late 2023, led to significant disruptions in Suez Canal operations. This geopolitical instability forced shipping companies to reroute vessels via the longer Cape of Good Hope, thereby increasing transit distances and operational costs. Quantitative analysis, as depicted in Fig. 6, indicates that during the first half of 2024, container freight rates on the MED route increased by approximately 130 % relative to the same period in 2023, while the NEUR route experienced an increase of about 226 %. These findings highlight the critical impact of exogenous geopolitical shocks on freight rate volatility. The discussion underscores that container freight rate determination is a complex interplay of inherent supply-demand dynamics and exogenous factors, including macroeconomic indicators and geopolitical risks. The integration of these diverse variables into our forecasting models not only enhances predictive performance but also offers significant insights for strategic decision-making in the maritime transport sector. Future research should further explore these interdependencies, particularly under conditions of heightened market volatility and geopolitical uncertainty, to develop more resilient and adaptive forecasting frameworks. 6. Conclusion Container freight rates play a pivotal role in logistics cost management and strategic decision-making within the shipping industry. The cyclical nature of ship ordering—where high freight rates prompt new orders that are delivered two to three years later, potentially leading to overcapacity and subsequent rate declines—exacerbates the inherent market volatility. Moreover, the increasing regulatory pressures to reduce carbon emissions have driven shipping companies to invest in eco-friendly vessels. Consequently, accurate forecasting of ocean freight rates becomes essential for effective risk management in an industry characterized by long-term planning and significant capital investments. This study undertook a comparative analysis of several forecasting models, including Decision Tree, Random Forest, LSTM, and Prophet, to determine their relative performance in predicting container freight rates. Our empirical results indicate that, in terms of absolute error metrics, both the Decision Tree and Random Forest models exhibit strong predictive capabilities. In this study, the model demonstrating the best overall performance was selected based on two evaluation approaches: (1) comparison of MSE, RMSE, NMSE, and MAE, and (2) comparison of MAPE and SMAPE. In the first evaluation, both the Random Forest and Decision Tree models exhibited strong performance, with Random Forest outperforming in some metrics. However, in the second evaluation using MAPE and SMAPE, the Decision Tree model was ultimately selected due to its relatively stable and superior performance across both indicators. These results highlight that the optimal model may vary depending on the chosen evaluation metric. Notably, the Decision Tree model emerged as the most effective when assessed using the relative error metric, MAPE and SMAPE, despite overall MAPE and SMAPE performance remaining suboptimal across all models. The elevated MAPE and SMAPE values can be attributed to the amplified impact of external shocks, particularly EPU and GPR, which have increasingly influenced market dynamics. This confirmation of the impact of EPU and GPR is expected to help the shipping industry stakeholders make decisions. The findings of this study underscore the critical influence of both traditional supply-demand factors and external economic and geopolitical shocks on freight rate forecasting. However, the persistence of relatively high prediction error ratios highlights a significant limitation of the current modeling approaches. This suggests the need for the development of more sophisticated hybrid models—potentially integrating approaches such as ANN and RNN—that are better equipped to capture the complex, non-linear interactions between exogenous factors Fig. 6. MED SCFI and NEUR SCFI (2023.01 – 2023.06 / 2024.01 – 2024.06). N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 105 and freight rate dynamics. Future research should focus on enhancing predictive accuracy by incorporating additional external variables and exploring ensemble methods that synergistically combine the strengths of various machine learning and deep learning models. Such advancements will be crucial for developing robust forecasting tools capable of supporting strategic decision-making in an increasingly volatile global shipping environment. CRediT authorship contribution statement Cha Junhee: Data curation, Formal analysis. Kim Namhun: Conceptualization, Data curation. Jeon Junwoo: Conceptualization, Formal analysis, Supervision. Declaration of Competing Interest The authors declare that there are no conflicts of interest regarding the publication of this paper. Appendix Fig. 7. The Influence of Feature (USWC), Random Forest Fig. 8. The Influence of Feature (USEC), Random Forest Fig. 9. The Influence of Feature (MED), Random Forest N. Kim et al. The Asian Journal of Shipping and Logistics 41 (2025) 99–109 106