Modeling the Ningbo Container Freight Index Through Deep Learning: Toward Sustainable Shipping and Regional Economic Resilience

Abstract

With the expansion of global trade, China’s commodity futures market has become increasingly intertwined with regional maritime logistics. The Ningbo Containerized Freight Index (NCFI), as a key regional indicator, reflects freight rate fluctuations and logistics efficiency in real time. However, limited research has explored how commodity futures data can enhance NCFI forecasting accuracy. This study aims to bridge that gap by proposing a hybrid deep learning model that combines recurrent neural networks (RNNs) and gated recurrent units (GRUs) to predict NCFI trends. A comprehensive dataset comprising 28,830 daily observations from March 2017 to August 2022 is constructed, incorporating the futures prices of key commodities (e.g., rebar, copper, gold, and soybeans) and market indices, alongside Clarksons containership earnings. The data undergo standardized preprocessing, feature selection via Pearson correlation analysis, and temporal partitioning into training (80%) and testing (20%) sets. The model is evaluated using multiple metrics—mean absolute Error (MAE), mean squared error (MSE), root mean square error (RMSE), and R²—on both sets. The results show that the RNN–GRU model outperforms standalone RNN and GRU architectures, achieving an R² of 0.9518 on the test set with low MAE and RMSE values. These findings confirm that integrating cross-market financial indicators with deep sequential modeling enhances the interpretability and accuracy of regional freight forecasting. This study contributes to sustainable shipping strategies and provides decision-making tools for logistics firms, port operators, and policymakers seeking to improve resilience and data-driven planning in maritime transport.

1. Introduction

Container transportation has contributed significantly to the development of international trade and global supply chains, now accounting for more than 60% of the global seaborne trade value [1,2,3]. The container shipping industry thus serves as a fundamental pillar of the global trade system, with its highly volatile freight rates primarily driven by fluctuations in shipping capacity and demand [4,5,6], significantly influencing trade liquidity and business decision-making [7,8,9,10]. In response to these dynamics, various container freight indices have been established. Among them, the NCFI, introduced in 2013 by the Ningbo Shipping Exchange, serves as a regional indicator reflecting freight rate trends at the port of Ningbo. Compared with national indices such as the China Containerized Freight Index (CCFI), the Shanghai Containerized Freight Index (SCFI), and the Baltic Dry Index (BDI), the NCFI focuses on actual transaction prices at a single port, offering greater timeliness and regional sensitivity [11]. Covering major trade routes such as Europe, North America (East and West coasts), and Southeast Asia, the NCFI is calculated using a weighted average approach, thereby enhancing market transparency and providing an important reference for enterprises, governments, and third-party institutions for pricing strategies and market analyses.

With increasing volatility in global trade patterns and policy shifts, the role of the NCFI has expanded to include market forecasting, floating contract pricing, and policy assessment [12]. Shipping companies frequently rely on the index for capacity planning and route optimization, while government bodies and industry associations use it in logistics performance monitoring systems [8,13]. In recent years, with China’s commodity futures market becoming more globally integrated [14,15], the NCFI has emerged as a key indicator of regional economic–shipping linkages, reflecting Ningbo Port’s responsiveness to futures price changes [7,16]. As a result, the NCFI has gained importance not only as a pricing reference tool but also as a strategic variable in international finance and regional policy research. It serves as a foundational element for constructing a more resilient and sustainable maritime supply chain. Exploring the dynamic link between China’s futures market and the NCFI is crucial for enhancing forecasting accuracy, advancing green logistics, and improving risk management [16,17,18].

While interest in freight index forecasting is rising, few quantitative studies explore the predictive link between China’s futures market and the NCFI. Existing research mainly focuses on (1) the BDI as a macroeconomic and trade indicator [19,20,21,22]; (2) links between container freight indices and commodity prices [23,24,25,26]; and (3) the impacts of freight rates on global trade, positioning freight indices as the leading indicator [20,27,28]. However, most studies fall short of capturing the unique characteristics of China’s regional markets. For example, as a crucial export hub, Ningbo is surrounded by manufacturing clusters, key export cities, and large-scale commodity markets, making it highly representative. Yet, the predictive potential of futures market dynamics for the NCFI in this regional context has largely been overlooked. Researchers have increasingly recognized that the NCFI, as a non-stationary and nonlinear time series, exhibits complex structural patterns and frequent volatility, which pose challenges for traditional econometric methods and limit their forecasting accuracy [16,17,18,19,20,21,22,23]. By contrast, machine learning models have demonstrated strong capabilities in capturing such complex time series behavior [29,30]. Nonetheless, single machine learning models often face limitations related to sample structure, model overfitting, and biased predictions [31]. Therefore, the development of a multivariate deep learning model that offers robustness, generalizability, and adaptability to environmental changes is crucial for improving NCFI forecasting accuracy and supporting the development of low-carbon, intelligent shipping systems. Building on this background, this study addresses two key questions:

• Which futures products or indicators effectively predict NCFI volatility trends?
• Which deep learning model best captures the dynamic, nonlinear, multivariate nature of NCFI forecasting?

To answer these questions, we propose a deep learning ensemble model that integrates RNN with GRU, referred to as the RNN–GRU model. This model is designed to explore the predictive mechanisms and influence of China’s commodity futures market on the NCFI. Using a dataset of 28,830 daily observations spanning from 24 March 2017 to 31 August 2022, we construct a time series forecasting framework centered around the RNN–GRU architecture. The model is capable of identifying long-term dependencies and dynamic features embedded in the NCFI series and demonstrates strong adaptability when facing challenges such as sample fluctuations, frequency variations, and structural discontinuities. The results show that the RNN–GRU model consistently outperforms standalone RNN and GRU models across multiple evaluation metrics, achieving a high prediction accuracy with an R² of 95.18%, thereby significantly improving the forecasting quality of the NCFI.

To the best of our knowledge, this is the first study to forecast the NCFI using data from China’s commodity futures market. Unlike previous research focused on global indices such as the BDI or SCFI, this study develops a hybrid RNN–GRU deep learning model tailored to capture the nonlinear, cross-market dynamics of the NCFI. By integrating over 28,000 daily observations and a wide range of futures and shipping variables, this model fills a key research gap and offers a novel, data-driven framework for sustainable and resilient freight forecasting.

This paper is structured as follows. Section 2 reviews the relevant literature; Section 3 outlines the data and the RNN–GRU model design; Section 4 compares results from GRU, RNN, and RNN–GRU models; and Section 5 concludes with implications, limitations, and future research directions. The overall research design and modeling procedure are illustrated in Figure 1.

2. Literature Review

2.1. The Application and Impact of the NCFI in Regional and Global Container Transport Markets

Although the industrial value of the NCFI has become increasingly prominent, systematic academic research on its modeling, forecasting, and structural evolution remains limited and exploratory. A number of scholars have initiated methodological explorations following a “construction–validation–optimization” approach, gradually establishing a representative research logic framework [32,33,34]. Given the strategic position of Ningbo Port in China’s foreign trade landscape and the significant impact of container freight volatility on regional economies, NCFI-related studies have gradually emerged as a key subfield within maritime finance and regional economic research. The existing literature has focused on the construction mechanisms of the NCFI, the evolution of computational methods, sensitivity analyses, and application expansion, and linkages with urban logistics systems and regional economic indicators.

In terms of model structure, Liu et al. [11] were among the first to propose a framework that draws on international experience to build a localized index system, covering the full process from data collection and indicator design to empirical validation. Later, Liu et al. [8] extended the index system to the Ningbo road freight market, proposing a hybrid modeling approach combining fixed-base and weighted average methods, which they validated through empirical analysis for land transportation applications. In terms of methodological innovation, Zhao et al. [12] introduced the internationally recognized Laspeyres Chain Index to replace the traditional simple aggregation method, enhancing the NCFI’s sensitivity and stability under conditions of structural change and price volatility. The study also incorporated turnover factors into the weighting mechanism and optimized indicator weights using correlation analysis, offering a new direction for dynamic index adjustment.

At the variable modeling level, Lin et al. [35] employed Spearman rank correlation analysis and vector autoregression models to examine the Ningbo container road freight market, identifying macro-variables highly correlated with freight volatility, such as total exports, energy costs, and labor expenditures. This revealed coupling relationships between container prices and regional economic cycles, supporting the use of multi-factor models in index construction. From the perspective of port system evolution, Ke and Oh [36] used port influence curves and the regional concentration index to explore the spatial interactions between Ningbo Port and the regional economy. They recommended differentiated infrastructure investment strategies tailored to different stages of development to enhance the spatial explanatory power of the index and the adaptability of regional sustainable logistics systems.

Feng [37], focusing on port-adjacent industrial clusters, analyzed their impact on transportation routes, cargo agglomeration, and multi-level cooperation networks, suggesting the creation of coordination mechanisms to improve Ningbo Port’s logistics efficiency. Sun et al. [38] applied the TOPSIS model to evaluate multimodal transport route optimization from Ningbo-Zhoushan Port to Southwest China, offering decision support for enhancing corridor resilience. Zeng et al. [39] used the COPRAS scoring method to develop an evaluation index system covering port infrastructure, smart logistics systems, and international capacity, conducting cross-sectional comparisons of Ningbo-Zhoushan Port’s logistics development while emphasizing a continuous improvement path oriented toward greening, digitalization, and internationalization. Jing and Jia-Wei [40] developed a logistics competitiveness assessment framework for Ningbo-Zhoushan Port using factor and cluster analysis, identifying key variables influencing core competitiveness through SPSS 28.0-based ranking. Deng et al. [41] adopted a modified gravity model to analyze both waterway and inland port connectivity hierarchically, revealing uneven port linkages within the Yangtze River Economic Belt and their core–periphery structural features.

Overall, the current literature has preliminarily developed a comprehensive analytical framework encompassing index construction, methodological evaluation, economic linkage, and system comparison. This provides a solid foundation for integrating intelligent forecasting technologies in the future, particularly in the context of sustainable supply chain management and green shipping strategies.

2.2. Linkage Between China’s Futures Market and the NCFI

Cross-Market Coupling: Structural Linkages Between Futures Prices and Shipping Freight Rates

With the rapid development of China’s commodity futures market, its role as an external driver in the formation of shipping prices has become increasingly significant [42]. Futures prices of major commodities such as crude oil, iron ore, and liquefied petroleum gas, as leading indicators of transportation costs, have gradually been incorporated into the NCFI’s predictive factor system [43,44,45,46,47]. Kavussanos et al. [48] highlight the existence of a notable cross-market linkage between futures and freight prices, arguing that this structural coupling can support risk warning systems, hedging mechanism design, and market stability assessment [49].

In addition, Feng, Grifoll, and Zheng [50] used an ARIMA model to forecast container throughput at Ningbo Port, verifying the strong correlation between macroeconomic fluctuations and transportation demand, indirectly supporting the feasibility of using futures prices as predictive variables. Sun et al. [38] and Zeng et al. [39], focusing on intelligent logistics systems and multimodal coordination efficiency, emphasized the need to construct comprehensive index systems that integrate financial variables, information indicators, and port timeliness metrics. These efforts aim to enhance the forward-looking functionality of the NCFI and its practical value within green and resilient logistics networks.

In recent years, as big data and artificial intelligence technologies have advanced, researchers have moved beyond traditional linear modeling to explore more flexible and interpretable nonlinear models for container freight forecasting [51]. Yu et al. [24] developed a neural network ensemble model incorporating Granger causality testing, confirming the leading role of futures markets in NCFI prediction. Chen et al. [25] proposed a hybrid CNN–LSTM architecture, demonstrating high robustness and generalization ability in decomposing the short-term fluctuations and trend patterns of the Shanghai Containerized Freight Index, significantly improving adaptability to non-stationary sequences. Schramm and Munim [4] continued to apply classic statistical methods, such as ARIMA, VAR, VECM, and artificial neural networks (ANNs), to predict China’s export freight index and introduced a Markov-switching model to characterize market volatility regimes. Chen et al. [52] developed an EMD-grey model to enhance interpretability by decomposing time series into trend and cyclical components. Han et al. [53] developed a CNN–LSTM model to forecast the BDI and CCFI based on Chinese financial market data, highlighting the connection between financial dynamics and sustainable maritime logistics.

The literature consistently shows that integrated models enhance forecasting accuracy across different time scales and input structures, serving as a key technical pathway to handle complex freight price fluctuation scenarios. Especially in the context of a global supply chain shift toward sustainability and smart logistics, models capable of nonlinear modeling and multi-source heterogeneous data integration offer greater practical value. Against this backdrop, this study introduces an innovative ensemble model that combines RNNs and GRUs to construct a dynamic forecasting framework linking high-frequency commodity futures data with regional shipping freight rates in China. The model demonstrates strong performance in capturing long-term dependencies, adapting to non-stationary fluctuations, and responding to sudden disturbances, making it particularly suitable for high-dimensional, nonlinear, cross-market tasks in sustainable freight index modeling.

2.3. Comparative Overview of Forecasting Models

To better illustrate the performance gap between traditional and advanced forecasting techniques, and to clearly position the proposed RNN–GRU model,

Table 1. Comparison of index forecasting methods.

Model Type	Key Features	Strengths	Limitations
ARIMA/VAR/VECM	Linear statistical models	Effective for stationary data; interpretable	Poor at capturing nonlinear and non-stationary patterns
ANN	Basic feedforward structure	Learns simple nonlinear relationships	Lacks sequence memory; limited temporal modeling
LSTM	Memory-based deep learning	Captures long-term dependencies; handles nonlinear data	Complex architecture; higher training cost
GRU	Gated mechanism; simplified LSTM	Fewer parameters; fast training; good for volatile data	May overlook short-term anomalies
RNN	Lightweight recurrent structure	Sensitive to short-term patterns	Suffers from vanishing gradients; weak long-term memory
RNN–GRU (Proposed Model)	Hybrid made of RNN and GRU layers	Balances short- and long-term dependencies; robust and adaptive	Requires hyperparameter tuning; lower interpretability

provides a comparative analysis of mainstream index forecasting models. The table summarizes their key features, advantages, and limitations in handling complex, nonlinear, and high-frequency time series data such as the NCFI. This structured overview highlights the challenges faced by conventional models and demonstrates how the RNN–GRU hybrid approach addresses these gaps with improved accuracy, adaptability, and robustness.

This comparative analysis justifies the selection of the RNN–GRU model as the optimal approach for modeling the dynamic and cross-market nature of the NCFI. By leveraging the complementary strengths of RNNs and GRUs, the model is capable of addressing both short-term volatility and long-term structural patterns, offering a resilient and scalable forecasting solution for regional freight indices.

3. Research Methods

3.1. Data Overview

The model constructed in this study is based on two core datasets: (1) data from China’s commodity futures market and (2) the NCFI, representing the dynamic evolution of the financial market and the regional container shipping market, respectively. The NCFI data, published by the Ningbo Shipping Exchange, reflect the actual freight rate changes of Ningbo Port’s export routes on a regular basis. The futures market data are sourced from the Dalian Commodity Exchange, the Shanghai Futures Exchange, and the Choice Financial Terminal, covering representative commodity futures traded in China’s domestic market.

The NCFI, launched by the Ningbo Shipping Exchange in 2013, is a regional freight rate indicator calculated based on the actual transaction prices of export container services from Ningbo Port. It covers 21 shipping routes across major global regions such as Europe, North America, and Southeast Asia. The index is computed weekly using a weighted average formula:

$${\mathrm{N}\mathrm{C}\mathrm{F}\mathrm{I}}_t=\sum _{i=1}^n w_i\cdot R_{i,t}$$

(1)

where $R_{i,t}$ represents the freight rate of route $i$ at time $t$, and $w_i$ denotes the fixed weight assigned to each route based on its cargo volume and market representativeness. The base period is set at 1000 points on 23 October 2013. The use of actual transaction prices ensures timeliness and sensitivity to real market fluctuations. Therefore, the correlation between the NCFI and futures variables reflects direct economic linkages between commodity markets and containerized shipping costs.

Selected variables include Clarksons containership earnings, major commodity futures (e.g., rebar, copper, gold, silver, iron ore, cotton, soybean, corn, and coal), and two market volatility indices—CSI 300 and SSE 50 Futures. These variables not only capture the general trends of bulk commodity prices in China’s futures market but also span critical sectors such as construction materials, industrial raw materials, agricultural products, and financial markets. This allows for a comprehensive representation of the operational status of China’s major industrial chains. For instance, rebar and iron ore prices are closely linked to the manufacturing and export processing industries; copper and silver are widely used in electronics manufacturing and the green energy sector; agricultural futures reflect the dynamics of the food supply chain and its role in the export system; and financial indices capture overall market sentiment and macroeconomic cycles.

Moreover, Clarksons average containership earnings serves as a key indicator of the global shipping market and complements the regional nature of the NCFI, enhancing the model’s generalization capability and predictive accuracy in cross-market modeling. These variables are closely related to the cost structure of China’s export supply chain and global supply–demand shifts, possessing strong economic representativeness and trend foresight. They also provide essential data support for exploring sustainable supply chains, green transportation pricing, and trade resilience.

The dataset spans from 24 March 2017 to 31 August 2022, comprising a total of 28,830 daily observations. This long time span and stable data frequency provide a robust foundation for training and developing the RNN–GRU deep learning model. The high-frequency, high-dimensional data structure offers strong support for complex nonlinear sequence modeling and long-term trend forecasting in this study (

Table 2. Variables for this research.

Variables	Symbol	Unit	Mean	Std. Dev.	Min	Max
Ningbo Container Freight Index	NCFI	Index	1331.33	857.06	632.36	3787.91
Clarksons Avg. Containership Earnings	CLAR	USD/day	22,323.34	25,558.10	6726.856	87,777.97
Rebar Futures	REBAR	CNY/Ton	4009.61	641.76	2920.00	5765.00
Copper cathode futures	COPPER	CNY/Ton	55,330.48	9653.86	38,380.00	74,840.00
Gold futures	GOLD	CNY/g	337.90	52.41	263.80	450.46
Silver futures	SILVER	CNY/kg	4330.09	713.00	3078.00	7752.00
Iron Ore Futures	IRON-ORE	CNY/Ton	649.21	200.47	423.00	1243.50
Cotton futures	COTTON	CNY/Ton	15,363.00	2713.02	10,735.00	21,910.00
Soybean No. 1 Futures	SOYBEAN	CNY/Ton	4574.07	1087.49	3139.00	7473.00
Corn Futures	CORN	CNY/Ton	2190.31	437.59	1718.00	3027.00
Thermal Coal Futures	THERMAL-COAL	CNY/Ton	662.69	152.42	494.80	1747.70
Coking coal futures	COKING-COAL	CNY/Ton	1575.72	543.31	943.00	3551.00
CSI 300 Futures Index	CSI300	CNY	4134.23	614.50	3003.60	5344.40
SSE 50 Futures Index	SSE50	CNY	2923.43	362.00	2292.60	4003.60

).

Figure 2 illustrates the line charts of the research variables from 24 March 2017 to 31 August 2022, visually reflecting the fluctuation patterns and evolutionary trends of each indicator over the past six years. These charts not only provide an intuitive understanding of the dynamic relationships between the NCFI and the related variables but also lay a solid foundation for subsequent modeling and empirical analysis.

In machine learning modeling, feature selection plays a crucial role in enhancing predictive accuracy and model interpretability. To ensure a robust input structure for NCFI forecasting, we conducted a systematic correlation analysis using Pearson coefficients. The resulting heatmap (Figure 3) visually illustrates the linear relationships between each candidate variable and the NCFI. Variables showing a weak or negligible correlation were excluded to reduce dimensionality, eliminate noise, and mitigate the risk of overfitting.

The key variables retained, such as REBAR, IRON-ORE, COPPER, COKING-COAL, CLAR, and CSI300, demonstrated both statistical relevance and strong economic interpretability. These indicators reflect upstream cost pressures, energy market volatility, and broader financial sentiment, aligning with the complex drivers of container freight rates. This targeted feature selection process not only improves generalization performance but also supports the development of a sustainability-oriented, data-driven forecasting framework.

The exploratory data analysis confirms several key aspects relevant to our research design. First, the correlation heatmap (Figure 3) reveals that several futures products, such as rebar, iron ore, copper, and coal, exhibit strong positive correlations with the NCFI, supporting the hypothesis that commodity futures prices are significant leading indicators of regional freight index volatility.

3.2. Model Construction and Architecture Design

3.2.1. RNN Model

An RNN is a type of neural network specifically designed for processing sequential data. Its core concept lies in a “memory mechanism” that retains historical information, enabling the network to incorporate the hidden state from the previous time step into the computation of the current time step. This allows the model to capture dependencies within time series data [54]. Unlike feedforward neural networks, the output of an RNN depends not only on the current input but also on past states, making it particularly suitable for tasks such as time series forecasting, speech recognition, and language modeling. The structure of an RNN is illustrated in Figure 4.

Here, $x$ represents the input, $s$ denotes the hidden layer units, and $o$ is the output. $U, V,$ and $W$ are the weight matrices for the input, output, and hidden layers, respectively. At time step $X_t$, the input is $X_i$, and the hidden layer output is calculated as:

$$s_t=f\left(U\cdot x_t+W\cdot S_{t-1}+b\right)$$

(2)

The final output of the model is:

$$o_t=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}\left(V\cdot S_t\right)$$

(3)

where $x_t$ is the input vector at time step $t;s_t$ is the hidden state at time $t;o_t$ is the output at time $t;U,W,$ and $V$ are weight matrices for the input, hidden, and output layers; $b$ is the bias vector; and $f$ is the nonlinear activation function.

The softmax function is a normalized exponential function.

While RNNs can theoretically handle sequences of any length, they often face vanishing or exploding gradient issues during backpropagation with long sequences. These problems make it difficult for the model to learn long-term temporal dependencies. To address this, researchers have developed various improved architectures, including LSTMs and GRUs. Standard RNNs are lightweight, efficient, and well-suited for capturing short-term patterns in high-frequency data. Therefore, this study integrates RNNs with GRU layers to enhance the detection of short-term fluctuations in the NCFI sequence.

3.2.2. GRU Model

The GRU is an improved recurrent neural network architecture proposed by Shewalkar [55]. It was designed to address the issues of vanishing gradients and low learning efficiency encountered by traditional RNNs when processing long sequence data. A GRU, a simplified version of the LSTM model, maintains gated mechanisms but has a more compact structure with fewer parameters. This results in faster training and makes it particularly suitable for modeling high-frequency, non-stationary time series data [56,57,58,59].

The core idea of a GRU is to dynamically regulate the retention and forgetting of information over time through two gating mechanisms: the update gate and the reset gate. The network structure is illustrated in Figure 5.

For this, $x_t$ is the input at time step; $h_{t-1}$ is the previous hidden state (output); and $h_t$ is the current output. The update gate $z_t$ is computed as follows:

$$z_t=\sigma \left(x_t{W}_{xz}+H_{t-1}{W}_{hz}+bz\right)$$

(4)

where $W_{xz}$ is the weight matrix and $b_z$ is the bias vector. The reset gate $r_t$ is calculated as:

$$r_t=\sigma \left(x_t{W}_{xr}+H_{t-1}{W}_{hr}+b_r\right)$$

(5)

where $W_{xr}$ is the weight matrix and $b_r$ is the bias vector. The GRU calculates the candidate activation $u_t$ as:

$$u_t=\tanh \left(W_u\cdot \left[r_t\times h_{t-1},x_t\right]+b_u\right)$$

(6)

where $W_u$ is the weight matrix and $b_u$ is the bias vector. The GRU output $h_t$ is calculated as:

$$h_t=\left(1-z_t\right)\times h_{t-1}+z_t^{\mathrm{*}}{u}_t$$

(7)

where $x_t$ is the input at time $t;h_{t-1},h_t$ are the previous and current hidden states; $z_t,r_t$ are the update and reset gates; ${\tilde{h}}_t$ is candidate activation; $\sigma$ is the sigmoid activation function; tanh is hyperbolic tangent activation; $W_{xz},W_{hz},W_{xr},W_{hr},$ and $W_u$ are weight matrices; and $b_z,b_r,$ and $b_u$ are bias terms with element-wise multiplication.

3.2.3. Criteria Importance Through Intercriteria Correlation (CITIC)

The CRITIC weighting method provides a scientific evaluation based on the inherent characteristics of the data. Suppose there are $n$ alternatives to be evaluated and $m$ evaluation criteria, forming a data matrix $X={\left(x_{ij}\right)}_{n\times m}$. Let $x_{ij}^{\prime }$ represent the standardized elements of the data matrix. The calculation steps are as follows:

(1)

Data standardization:

For benefit (positive) criteria, the standardized value is calculated as:

$$x_{ij}^{\prime }={\displaystyle \frac{x_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_1,x_2,\cdots ,x_{nj}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_1,x_2,\cdots ,x_{nj}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_1,x_2,\cdots ,x_{nj}\right)}}$$

(8)

For cost (negative) criteria, the standardized value is calculated as:

$$x_{ij}^{\prime }={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_1,x_2,\cdots ,x_{nj}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_1,x_2,\cdots ,x_{nj}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_1,x_2,\cdots ,x_{nj}\right)}}$$

(9)

(2)

Calculate the standard deviation of each criterion:

$$\begin{array}{c}{\bar{x}}_j={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n} x_{ij}\\ S_j=\sqrt{{\displaystyle \sum _{i=1}^n} {\displaystyle \frac{{\left(x_{ij}-{\bar{x}}_j\right)}^2}{n-1}}}\end{array}$$

(10)

where $S_j$ represents the standard deviation of the $j$-th criterion.

(3)

Calculate the correlation coefficient:

$$R_j=\sum _{i=1}^p \left(1-r_{ij}\right)$$

(11)

where $r_{ij}$ epresents the correlation coefficient between criteria $i$ and $j$.

(4)

Calculate the total information $C_j$ of each criterion:

$$C_j=S_j\sum _{i=1}^p \left(1-r_{ij}\right)$$

(12)

(5)

Calculate the weight $W_j$ of the $j$-th criterion:

$$W_j={\displaystyle \frac{C_j}{\sum _{i=1}^p C_j}}$$

(13)

3.2.4. Construction of the RNN–GRU Hybrid Prediction Model

The RNN–GRU model combines the long-term memory capability of GRUs with the sensitivity of RNNs to local temporal features, forming a hybrid deep learning architecture that is well-suited for both long-term trend modeling and short-term disturbance handling. In this study, the NCFI, as a regional container export price index, exhibits significant nonlinear volatility, cyclical jumps, and sensitivity to macroeconomic factors. Its fluctuations are influenced not only by supply and demand changes in domestic and international trade but also by commodity prices, policy adjustments, and global events such as pandemics, wars, and inflation. A single neural network model often struggles to fully capture the multi-layered characteristics of such complex sequences. In contrast, the RNN–GRU model structurally enables the effective decomposition and integration of these features.

Specifically, the GRU component leverages gating mechanisms to dynamically filter and update historical input states, making it suitable for extracting medium- to long-term trends, seasonal patterns, and lag effects. This helps the model establish a stable foundational framework for time series prediction. The subsequent RNN layer enhances the model’s responsiveness to recent high-frequency fluctuations and abnormal disturbances, thereby improving its adaptability to short-term price changes. Prioritizing long-term patterns followed by short-term features notably improves the model’s robustness and generalizability.

In addition, due to the GRU having fewer parameters and faster convergence during training and the RNN’s relatively simple structure and ease of tuning, the entire model maintains high prediction accuracy while achieving excellent computational efficiency. This makes it particularly suitable for modeling high-dimensional, multivariate, and long-span datasets. Therefore, the RNN–GRU model is an ideal architecture for handling complex, high-frequency economic time series such as the NCFI. It can significantly improve prediction accuracy, stability, and practical utility while also offering a replicable modeling paradigm for regional shipping economic analysis.

In this study, a hybrid prediction model based on the GRU and RNN models is constructed to forecast the NCFI. The network structure is shown in Figure 6.

The network architecture is set to three layers: the first layer uses a GRU structure, while the second and third layers adopt RNN structures.

3.2.5. Model Evaluation Metrics

This study employs five evaluation metrics to assess model performance: the RMSE, MAE, MSE, coefficient of determination for the training set (R²), and coefficient of determination for the test set (R²).

3.2.6. Implementation Details

The RNN, GRU, and RNN–GRU models were implemented in Python 3.9 using the TensorFlow 2.12 and Keras deep learning libraries. All experiments were conducted on a Windows 11 workstation equipped with an NVIDIA RTX 3060 GPU (12 GB), 32 GB RAM, and an Intel Core i7 processor. The models were trained using the Adam optimizer with a learning rate of 0.001, a batch size of 32, and the mean squared error as the loss function. Early stopping with a patience of 10 epochs was applied to prevent overfitting. All data preprocessing, including standardization and correlation analysis, was conducted using the Pandas and Scikit-learn libraries.

4. Model Results and Comparative Analysis

4.1. Data Processing

In this study, we adopted a rigorous data processing strategy by dividing the dataset into three phases: training, validation, and testing. Each phase played a critical role in evaluating and optimizing the performance of the RNN, GRU, and RNN–GRU models.

To fully capture the complex dynamic characteristics of the NCFI and ensure the accuracy and generalization capability of the validation and test results, we partitioned the data based on time series, ensuring that each subset originates from a continuous time window. The training set includes the earliest data to capture historical trends, the validation set monitors performance on unseen data for tuning, and the test set uses the most recent data to assess the model’s predictive accuracy.

Considering the abnormal fluctuations in the market during the COVID-19 pandemic, we used the first 80% of the data for training and the remaining 20% for testing. A unified preprocessing procedure was applied before modeling. This time-based partitioning approach ensures the model has sufficient exposure to historical information while enhancing its ability to adapt to future market changes.

4.2. Data Processing Overview

We conducted a detailed comparative analysis of the three models—RNN, GRU, and RNN–GRU—aiming to evaluate their effectiveness in forecasting the NCFI. A series of charts were created to visualize each model’s performance on different datasets, including quantitative loss function (mean squared error) analysis on both the training and test sets. In addition to showing the models’ predictions on the training set, we also compared their predictions on the test set with the actual values to provide a concise summary of overall performance.

We examined the loss curves of the three models (Figure 7, Figure 8 and Figure 9) to evaluate fitting performance. Underfitting is indicated when the validation loss exceeds the training loss; overfitting is marked by a rising or significantly higher validation loss. A good fit is reflected by closely aligned loss curves. In the figures, the Y-axis denotes loss and the X-axis represents iterations, with training loss in blue and test loss in red. These visualizations provide a clear view of each model’s training and validation process, allowing us to assess and compare their predictive capabilities.

In addition, we summarized the prediction results of the RNN, GRU, and RNN–GRU models on the training set (Figure 10), validation set (Figure 11), and test set (Figure 12) to provide a brief overview of their overall performance. The results show that the RNN–GRU model outperforms the other two.

After completing the model training and testing, this study systematically evaluated and conducted a multi-dimensional analysis of the RNN–GRU model’s performance in forecasting the NCFI. By comparing the fit between the predicted and actual values, we could preliminarily observe whether the model has a stable trend-tracking ability and short-term fluctuation-capturing capability.

Figure 12 shows that the RNN–GRU model surpasses the RNN and GRU models in overall accuracy and prediction performance. In most time periods, it is able to closely fit the true trajectory of the NCFI, especially during periods of intense index fluctuations or when the market is rapidly rising or falling. The prediction curve remains relatively tightly aligned with the actual data. This indicates that the model has strong structural adaptability and predictive sensitivity when dealing with non-stationary, highly volatile shipping price time series data, demonstrating its outstanding potential for applications in complex market dynamics.

4.3. Model Evaluation

We evaluate model performance using the MSE and the coefficient of determination (R²), defined mathematically as follows:

$$\begin{array}{c}MSE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n} {\left(y_i-{\widehat{y}}_l\right)}^2\\ R^2=1-{\displaystyle \frac{\sum _{i=1}^n {\left(y_i-{\widehat{y}}_l\right)}^2}{\sum _{i=1}^n {\left({\overline{y}}_l-{\widehat{y}}_l\right)}^2}}\end{array}$$

After 100 simulation runs, the average R² scores on training and test sets were computed. As shown in

Table 3. Model accuracy evaluation.

Model	MSE	MAE	RMSE	R2 (Training)	R2 (Test)	MAPE (%)
GRU	8,525,712.0512	2885.9519	2919.8822	0.9817	0.8636	14.6820
RNN	9,233,648.5176	2986.8185	3003.5315	0.9894	0.9145	12.2078
RNN–GRU	8,996,423.9799	2998.8031	2998.9124	0.9963	0.9518	7.0704

, the RNN–GRU model achieved the best performance with an R² of 95.18%.

This study also uses common regression metrics—R², RMSE, and MAE—to quantitatively evaluate the model’s prediction accuracy on the test set. The RNN–GRU model performs exceptionally well, with an R² value of 0.9518, indicating that it explains over 95% of the variance in the actual data. Both the RMSE and MAE remain at low levels, reflecting minimal error fluctuations and stable, reliable predictions (Table 3). The RNN–GRU model shows clear advantages over the standalone GRU and RNN models in all metrics. Notably, during periods of high volatility, the RNN–GRU model more accurately identifies peaks and turning points, while traditional models often lag or suffer from distortion.

In summary, the RNN–GRU model exhibits significant technical advantages and adaptability when forecasting regional container freight indices such as the NCFI, which are characterized by cyclicality, jumps, and economic interdependencies. Its deep memory structure captures macro trends, while its sequence-sensitive mechanism responds to micro fluctuations, making it an effective approach for modeling high-frequency economic indicators. Using comparisons with traditional methods, this study further highlights the feasibility and cutting-edge potential of applying deep learning to regional shipping index forecasting, providing a valuable framework for future multi-index and multi-factor prediction tasks.

5. Discussion and Conclusions

The NCFI is an important indicator for measuring the operational status of regional export markets and price fluctuations in international logistics channels. It has gradually become one of the core parameters for assessing global supply chain resilience and China’s export vitality. Despite the increasing number of studies on container freight index forecasting in recent years, as noted by Munim and Schramm [60], Yu et al. [24], and Chen et al. [25], related research has mainly focused on national indices (e.g., the SCFI) or international indices (e.g., the BDI). A research gap remains in accurately modeling and forecasting regional indices, especially the NCFI. This study combines China’s commodity futures market with global shipping data to develop a deep learning ensemble model (RNN–GRU), integrating the GRU gating mechanism with the RNN structure to predict NCFI trends. This approach not only overcomes the limitations of traditional models in dealing with non-stationary, volatile time series but also addresses the limitations of studies such as that of Chen et al. [25], which had single-dimensional input and weak model adaptability. Compared to the EMD-ARMA model used by Chen et al. [52], the model in this study emphasizes the extraction of nonlinear features and the hierarchical modeling of short-, medium-, and long-term trends. Unlike the combination strategy based on practical experience employed by Schramm and Munim [4], this study adopts a data-driven, cross-market fusion approach, enhancing the model’s adaptability and generalizability.

In terms of variable selection, this study integrates key Chinese futures such as rebar, copper, iron ore, gold, and soybeans with the Clarksons global shipping earnings index as input variables, establishing an integrated factor system that spans both financial and shipping markets. This multi-dimensional data fusion model, which includes energy, metals, agricultural products, and financial indices, enhances the model’s ability to capture regional industrial linkages, supply–demand elasticity, and the transmission mechanisms of shipping costs. This helps to create a more sustainable and resilient logistics forecasting framework. Unlike Lin et al. [35], which built a VAR model based solely on regional economic data, this study simplifies the model structure and improves interpretability and operability by using Pearson correlation heatmaps to identify high-impact factors. Based on 28,830 data points from the futures market and shipping data from 24 March 2017 to 31 August 2022, a stable and efficient RNN–GRU model was constructed. In terms of model structure, the GRU module is responsible for extracting long-term trends and lag effects, while the RNN module enhances responsiveness to high-frequency disturbances and sudden events such as pandemics, wars, and inflation. The empirical results show that the RNN–GRU model performs optimally in NCFI forecasting, with an R² of 0.9518 on the test set, far exceeding traditional RNNs (0.9145) and GRUs (0.8636), validating its robustness and generalization ability when dealing with regional, highly volatile, and non-stationary data. This model is especially suitable for emerging practice scenarios such as green port logistics, sustainable transportation strategies, and dynamic risk management. Moreover, this study also addresses the gaps in the research of Yu et al. [24] and Chen et al. [52] regarding the “prospective impact mechanism of futures prices on shipping freight rates”. It is the first to empirically reveal the transmission path of Chinese futures market prices as economic signals in the formation of regional freight rates. This finding not only deepens the understanding of the complex interactions within the shipping–financial system but also provides a theoretical basis for building a sustainable, data-driven maritime economic governance system.

5.1. Theoretical Contributions

This study offers several theoretical contributions to the literature on freight index forecasting and maritime data modeling. First, while many existing studies have concentrated on global or national shipping indices such as the BDI [24,53,60], this study focuses on the NCFI, a regional indicator that remains relatively underexplored. By selecting the NCFI as the forecasting target, this research supports ongoing interest in region-specific logistics analysis and the relevance of localized freight behavior in international trade studies [16,35].

Second, the application of a hybrid RNN–GRU model adds to the growing use of deep learning methods in time series forecasting, particularly in maritime economics. The structure combines recurrent networks with gated mechanisms, helping to capture both long-term dependencies and short-term fluctuations in freight index movements. This modeling approach complements existing statistical and machine learning frameworks used in similar contexts [25,29] and contributes to the broader conversation about applying adaptive models to complex transport datasets.

Third, by incorporating futures market data, such as rebar, iron ore, and coal futures, into the forecasting process, this study reflects the close linkage between commodity prices and container freight rates. This supports prior work suggesting that freight pricing can be influenced by upstream market expectations and financial signals [48,61]. The inclusion of futures indicators contributes to a more integrated view of how financial and logistics variables interact over time.

Finally, the use of correlation-based feature selection introduces a level of transparency to the modeling process, helping to balance model complexity with interpretability. This aligns with current discussions on the need for more explainable AI models in transport and logistics research [4,10], especially when applying machine learning tools in policy-relevant contexts.

5.2. Managerial Contributions

From a managerial practice perspective, the findings of this study hold significant reference value for shipping companies, financial institutions, and government agencies.

For shipping companies, high-precision NCFI forecasting can provide decision support for scheduling, space allocation, freight pricing strategies, and cost control. By incorporating futures price variables into freight rate prediction logic, companies can more acutely sense upstream resource cost changes, allowing them to optimize contract pricing and cargo scheduling strategies. This enhances operational efficiency and profitability, especially in port and shipping management scenarios focused on “green transformation” and “carbon accounting” requirements.

For financial institutions, as a core market indicator, the NCFI’s dynamic changes not only influence the design of shipping derivatives (e.g., freight rate insurance and option contracts) but also serve as a crucial reference for risk control and asset evaluation. Accurate NCFI forecasting helps identify industry-specific risk exposures in advance and capture arbitrage opportunities, improving the pricing science and market stability of shipping financial products.

For policymakers, the NCFI can serve as a sensitive signal for regional foreign trade prosperity and global economic fluctuations. The model’s outputs can assist governments in real-time monitoring of transportation network stress levels and export channel activity, optimizing logistics infrastructure layout and policy response timing. For example, during disruptions such as pandemics or geopolitical conflicts, the model’s forecasting results can assess the impact on key industries, supporting the promotion of green port transformation, guiding reasonable freight rate fluctuations, and implementing sustainable shipping policies.

In summary, the RNN–GRU model proposed in this study not only provides an effective tool for regional freight rate forecasting but also fosters the collaborative interaction of shipping management, financial modeling, and policymaking in the context of data intelligence. This research supports the construction of a more adaptive and sustainable global logistics system.

5.3. Limitations and Future Directions

Although this study has made notable progress in forecasting the NCFI, several limitations should be acknowledged. First, the input variables are primarily drawn from commodity futures data and do not yet incorporate macroeconomic indicators, exchange rate fluctuations, port congestion levels, carbon emission regulations, or external shocks such as pandemics. These factors may exert a significant influence on freight rates, and future research could benefit from integrating broader sustainability and policy-related variables to improve the explanatory power of the forecasting model.

Second, the dataset used in this study covers the period from 24 March 2017 to 31 August 2022 due to limitations in the availability and accessibility of updated NCFI data at the time of analysis. Although the selected period includes a range of significant market events, including trade fluctuations and the COVID-19 pandemic, it may not fully capture the most recent shifts in the shipping sector.

Third, some of the data are sourced from public platforms and contain missing values or inconsistencies that may affect model training. Future research could explore the use of multi-source heterogeneous data fusion and advanced imputation techniques to improve data quality and robustness. Moreover, while the RNN–GRU model exhibits strong performance in this study, its tuning process requires substantial domain and modeling expertise. Future work may consider using automated approaches such as neural architecture search or Bayesian optimization to improve scalability and adaptability.

Finally, developing an interactive forecasting platform that integrates expert knowledge, scenario simulation, and risk analysis would help translate research into practical tools for decision-making. Such a system could provide real-time updates, visualization, and adaptive planning features, supporting smarter and more sustainable port and logistics operations.