Shipping News Sentiment Meets Multiscale Decomposition: A Dual-Gated Deep Model for Baltic Dry Index Forecasting

Abstract

Accurate prediction of shipping freight indices, represented by the Baltic Dry Index (BDI), is crucial for operational decision-making and risk management in the shipping industry. Existing models mainly rely on historical time-series data and often overlook the influence of unstructured information such as market sentiment. To address this limitation, this study proposes a dynamic freight rate prediction framework integrating a shipping text sentiment index. First, a shipping news sentiment index is constructed using a RoBERTa-based pre-trained model to quantify the impact of market sentiment on freight rate fluctuations. Second, the BDI series is decomposed and reconstructed through Variational Mode Decomposition (VMD) and Fuzzy C-Means (FCM) clustering to extract multiscale features. Finally, a deep learning based multi-step prediction model is developed by incorporating the sentiment index into the forecasting process. Empirical results show that the proposed model significantly outperforms benchmark models without sentiment information in terms of MAE, RMSE, and R², and demonstrates greater robustness under extreme market conditions. These findings provide a novel methodological framework for improving freight rate forecasting accuracy and offer practical decision support for shipping enterprises.

1. Introduction

The continuous escalation of global economic uncertainty, coupled with frequent geopolitical conflicts and public events, has intensified volatility in the shipping market, a core pillar of international trade. Fluctuations in freight rates directly affect transportation costs, supply chain stability, and investment decisions across global commodity markets. As a widely recognized barometer of dry bulk shipping activity, the Baltic Dry Index (BDI) reflects the balance between shipping demand and fleet capacity and is therefore closely monitored by market participants, policymakers, and researchers. Improving the understanding and forecasting of BDI dynamics is of substantial practical and academic importance, particularly in periods of heightened uncertainty.

Forecasting the Baltic Dry Index (BDI) has long been challenged by pronounced nonlinear behavior, time-varying dynamics, and strong sensitivity to external shocks. Early studies typically relied on econometric and volatility-oriented frameworks that model BDI dynamics primarily from historical freight rates and related structured market variables, aiming to capture persistence and cyclical behavior in shipping markets (e.g., Chen et al. [1]; Abakah et al. [2]). However, empirical evidence increasingly suggests that such approaches struggle to maintain predictive accuracy when market conditions deviate sharply from historical patterns, particularly under major economic events and policy-induced disruptions [1,3]. This limitation has motivated a growing body of research seeking more adaptive and information-rich forecasting paradigms.

To overcome these limitations, subsequent studies have progressively extended traditional frameworks by enhancing feature representation and information sources. Wu et al. [4] combined signal decomposition with probabilistic modeling to alleviate structural instability and forecast uncertainty in BDI series, while Zhang et al. [5] introduced a dynamic fluctuation network coupled with artificial intelligence techniques to explicitly capture evolving volatility structures, particularly under extreme market conditions. Complementary evidence indicates that incorporating external market information further improves predictive performance. Su et al. [6] demonstrated that commodity futures data significantly enhance BDI forecasting accuracy through a CNN–BiLSTM ensemble, and Bouri et al. [7] showed that low-frequency climate indicators such as ENSO provide incremental predictive power when integrated into mixed-frequency forecasting models.

Methodologically, decomposition-based forecasting frameworks have gained prominence as an effective means of handling multiscale and nonstationary characteristics in freight-related time series. Variational mode decomposition and related techniques have been widely integrated with deep learning models to enhance prediction stability and robustness [8,9]. Extensions of this paradigm to multi-step forecasting further demonstrate that decomposition-assisted deep learning frameworks outperform conventional approaches when prediction horizons are extended, with similar long-horizon forecasting architectures also reported in other domains [10,11,12]. Similar conclusions have been reported in other high-volatility domains, where adaptive decomposition and denoising strategies improve forecasting reliability under noisy conditions [13]. These studies collectively indicate that decomposition is not merely a preprocessing step but a key component for constructing multiscale representations suitable for long-horizon prediction.

In parallel, recent research has explored the intrinsic complexity and predictability limits of time series to support complexity-aware modeling strategies. Related evidence from financial markets further suggests that explicitly modeling dynamic dependence structures through network-based and copula-based frameworks can substantially improve volatility forecasting performance in complex systems [14]. Entropy-based analyses have been used to quantify the upper bounds of short-term predictability in complex systems [15], while hybrid frameworks combining optimized decomposition with deep learning and uncertainty quantification demonstrate improved robustness for highly complex sequences [16]. From a broader perspective, comprehensive reviews of shipping economic forecasting highlight a clear methodological evolution toward hybrid, AI-driven, and information-enriched models, while also noting the continued dominance of structured historical variables in most existing frameworks [17].

Beyond structured quantitative data, the price dynamics and forecasting literature provides compelling evidence that incorporating unstructured textual information into predictive models yields forward-looking insights unavailable from historical prices alone [18]. In particular, market sentiment extracted from text has been shown to contain predictive information for asset prices and trading behavior [19], motivating the construction of sentiment indices as forecasting inputs. Recent studies also emphasize the value of integrating sentiment indicators, non-traditional signals, and behavioral factors with machine learning to improve predictive accuracy in financial markets [20]. Subsequent research has shown that sentiment effects are inherently dynamic and scale-dependent, with time–frequency analyses revealing heterogeneous impacts across different horizons [21,22]. Advances in modeling frameworks further integrate sentiment into ensemble learning and data-driven prediction systems, improving both accuracy and interpretability under volatile market conditions [23,24]. More recently, domain-adapted language models, such as fine-tuned BERT variants, have been shown to substantially enhance the quality and predictive value of sentiment indices compared with traditional lexicon-based approaches [25].

Building on these methodological advances, sentiment analysis has been increasingly applied to shipping and freight markets. Bai et al. [26] constructed a shipping sentiment index from news coverage and provided early empirical evidence of its predictive relevance for dry bulk freight rates. This line of research was extended by Sui et al. [27], who employed market-specific language models and demonstrated that dry bulk market sentiment Granger-causes the BDI, outperforming conventional sentiment measures. Further studies revealed nonlinear and state-dependent relationships between shipping sentiment and freight rates, particularly in iron ore transportation markets [28]. In related work, textual sentiment has also been integrated with system dynamics and supply chain models to enhance freight rate forecasting under disruption scenarios [29].

Taken together, existing studies demonstrate substantial progress in modeling the nonlinear and multiscale characteristics of the Baltic Dry Index and in incorporating sentiment-based information into freight market forecasting. However, most existing approaches remain predominantly centered on historical freight time-series data and structured explanatory variables. While effective in capturing past market dynamics, such frameworks often exhibit lagged responses to rapidly evolving market conditions and provide limited insight into shifts in market sentiment. Moreover, sentiment information is typically introduced in a homogeneous manner, with insufficient consideration of how its predictive role may vary across different levels of time-series complexity or forecasting horizons. These limitations underscore the need for more sensitive, forward-looking, and complexity-aware analytical frameworks for BDI prediction.

In response to these limitations, this study introduces the integration of sentiment data with multiscale decomposition and complexity-aware models, developing a sentiment-based forecasting framework for the BDI. Specifically, building upon existing literature, the study constructs a shipping market sentiment index from news data and incorporates a sentiment gating mechanism, which explicitly accounts for the heterogeneity in time-series complexity. This key innovation aims to enhance the sensitivity and robustness of multi-step BDI predictions under volatile market conditions.

2. Methods

2.1. Research Approach

This study aims to improve the prediction accuracy of shipping freight rate indices by leveraging the complementary informational advantages of structured freight rate data and unstructured textual data to develop a comprehensive technical framework. The research is divided into two core phases: (1) Focusing on data preprocessing and feature engineering, this phase completes the construction of sentiment indices, the decomposition and reconstruction of the BDI series, and complexity assessment; (2) Focusing on the development of prediction models, this phase involves building separate models for low- and high-complexity components, integrating sentiment features via a gating mechanism, and finally systematically validating the models’ practical predictive performance through a combination of performance comparison and case analysis. Figure 1 illustrates the technical framework and complete implementation process of this study.

2.2. Data Collection and Preprocessing

This study constructs and analyzes two datasets: historical observations of the BDI and a corpus of shipping-industry-related news headlines.

The BDI serves as a benchmark indicator of conditions in the global dry bulk shipping market. The index is published by the Baltic Exchange in London and is released on all working days throughout the year. Movements in the index encapsulate changes in freight rates and transportation demand for key bulk commodities, including iron ore, coal, and grain, and thus provide a timely reflection of shipping market cycles, supply chain dynamics, and underlying macroeconomic activity. Given its established role in both academic research and industry practice, the BDI is employed as a proxy for fundamental market conditions in the shipping sector. The sample covers the period from November 2019 to January 2025 and consists of 1888 daily observations, capturing multiple phases of market expansion and contraction. Due to the inherent gaps in the BDI release schedule, linear interpolation is applied to fill in the missing values, ensuring a continuous and coherent time series for analysis.

Shipping sentiment is quantified using news headline data drawn from industry-specific media sources. News headlines are concise linguistic representations of underlying events and typically exhibit a clear evaluative orientation. Relative to full-text articles, headlines more directly convey sentiment while avoiding the semantic ambiguity and contextual dependency inherent in longer narratives, thereby enhancing their suitability for natural language processing applications.

Headline data are collected from several authoritative and highly specialized shipping information platforms, including China Shipping Network, China Water Transport Network, Port Information Network, and Logistics Baba. The news corpus is classified into three thematic categories: maritime transportation, port operations, and logistics systems. A multi-stage screening procedure is implemented, combining keyword-based semantic filtering with manual verification, to exclude non-informative content such as personal interviews and promotional materials. Following data cleaning and preprocessing, the final dataset comprises 53,650 news headlines published between 4 November 2019 and 3 January 2025, providing a robust textual foundation for the construction of the cumulative shipping sentiment index.

2.3. Construction of the Cumulative Shipping Sentiment Index

2.3.1. Sentiment Quantification Model

1.

Manual Annotation Procedure

Shipping-related news headlines contain extensive industry-specific terminology and nuanced semantics, rendering generic sentiment analysis tools inadequate for extracting market-relevant signals. Accordingly, a three-category sentiment scheme (positive, negative, and neutral) is constructed, where positive sentiment reflects favorable market information (e.g., freight rate increases or supportive policies), negative sentiment captures adverse shocks (e.g., freight rate declines or supply chain disruptions), and neutral sentiment corresponds to informational content without a clear emotional orientation. Manual labeling is performed by three annotators with expertise in shipping economics using a two-stage cross-labeling and adjudication protocol, preceded by annotator calibration. Two annotators independently assign labels, with disagreements resolved by a third reviewer. Inter-annotator reliability, assessed using Cohen’s Kappa coefficient, equals 0.84 in a pilot sample and remains above 0.80 for the full dataset, indicating robust labeling consistency.

2.

Sentiment Quantification Based on a RoBERTa Pretrained Model

The sentiment quantification model is constructed using manually annotated shipping news headlines and a RoBERTa pretrained language model, whose core architecture is based on a Transformer encoder composed of stacked self-attention and feed-forward layers. Given an input sequence X ∈ R^n×d, where n denotes the sequence length and d the embedding dimension, linear projections are applied to generate the query, key, and value matrices Q, K, and V. Self-attention weights are computed via scaled dot-product attention, as defined in Equation (1), where W_Q, W_K, and W_V ∈ R^d×dk are learnable parameter matrices and d_k denotes the feature dimension.

$$\mathit{Attention}(Q, K, V)=\mathit{Softmax}\left({\displaystyle \frac{Q{K}^{\top }}{\sqrt{d_k}}}\right)V$$

(1)

To capture semantic information from multiple representation subspaces, multi-head attention is employed by concatenating the outputs of parallel attention heads and applying a linear transformation, as specified in Equations (2) and (3), where W_O denotes the output projection matrix.

$${\mathit{head}}_i=\mathit{Attention}(Q{W}_Q^{(i)}, K{W}_K^{(i)}, V{W}_V^{(i)})$$

(2)

$$MultiHead(X)=\mathit{Concat}({\mathit{head}}_1,\dots , {\mathit{head}}_h)W_O$$

(3)

The attention outputs are subsequently processed by position-wise feed-forward networks with GELU activation, combined with residual connections and layer normalization, forming a deep contextual representation framework.

During pretraining, contextual semantic features are learned through a masked language modeling objective, formalized in Equation (4), where M denotes the set of masked positions, $y_t$ the corresponding ground-truth tokens, and $X_M$ the masked input sequence.

$$L_{MLM}=-{\displaystyle \frac{1}{\left|M\right|}}{\displaystyle \sum _{t\in M}\log }{P}_{\theta }(y_t\mid X_M)$$

(4)

For the downstream shipping news sentiment classification task, the RoBERTa model is fine-tuned on the labeled dataset. The data are stratified and split into training, validation, and test sets following an 80–10–10 ratio. Headlines are tokenized using the RoBERTa tokenizer, with a maximum sequence length set to 128; sequences exceeding this length are truncated, while shorter sequences are padded with [PAD] tokens to ensure batch-wise input consistency. On top of the pretrained encoder, two fully connected layers and a Dropout layer are added to mitigate overfitting. Sentiment labels are discretized into negative, neutral, and positive classes, and supervised learning is conducted using a cross-entropy loss function. Model training is implemented in a GPU environment using the roberta-base-chinese pretrained model from the Hugging Face Transformers library, optimized with the AdamW optimizer and augmented by early stopping and learning-rate scheduling strategies. In the inference stage, predicted class probabilities are transformed into a continuous sentiment polarity score in the interval $\left[-1,1\right]$ using a linear weighting scheme, as defined in Equation (5).

$$s_i=p_{positive} \times 1+p_{neutral }\times 0+p_{negative }\times \left(-1\right)$$

(5)

3.

Performance Comparison and Evaluation of Sentiment Quantification Models

Considering the characteristics of shipping news, where positive sentiment headlines are more frequent and neutral headlines are relatively sparse, the dataset exhibits class imbalance. To address this, Weighted-F1 is primarily used as the evaluation metric, as it accounts for class imbalance by weighting each class’s performance according to its frequency. Macro-F1 and Accuracy are also reported to provide a comprehensive evaluation of the model’s performance.

A set of benchmark models is employed for comparative analysis, encompassing both traditional text modeling approaches that rely on static word embeddings or local sequence features and pretrained BERT-type models that learn dynamic contextual representations from large-scale corpora. All models are trained and evaluated under identical experimental settings, including the same text preprocessing pipeline, training data, and hyperparameter configurations, to ensure result comparability.

As reported in

Table 1. Performance comparison of sentiment quantification models.

Model	Train Loss	Weighted-F1	Macro-F1	Accuracy
Word2Vec_MLP	0.3151	0.8821	0.8500	0.8811
FastText	0.3364	0.8811	0.8458	0.8825
TextCNN	0.2018	0.9320	0.9137	0.9312
BiLSTM	0.2651	0.9256	0.9062	0.9244
BERT	0.0764	0.9669	0.9578	0.9666
RoBERTa	0.0672	0.9696	0.9615	0.9693

, the Word2Vec-MLP and FastText models exhibit comparable but relatively limited performance, reflecting the inability of static word embeddings to capture contextual semantics and domain-specific polysemy prevalent in shipping news. Models incorporating sequential modeling mechanisms, such as TextCNN and BiLSTM, achieve notable performance improvements; however, TextCNN is constrained to local feature extraction, while BiLSTM remains limited in modeling long-range dependencies. Consequently, both models underperform relative to pretrained language models. Leveraging bidirectional Transformer-based contextual encoding, the BERT model delivers substantial gains in both classification accuracy and overall fit. RoBERTa further strengthens semantic representation learning and consistently outperforms all benchmark models across evaluation metrics, confirming its superiority for sentiment classification in shipping-related news. Notably, RoBERTa effectively addresses class imbalance while preserving strong overall classification performance. By strengthening semantic representation learning, it consistently outperforms all benchmark models, confirming its superiority in sentiment classification for shipping-related news.

2.3.2. Cumulative Sentiment Index

Market sentiment in the shipping industry does not arise from isolated news items but reflects the cumulative influence of multiple events over time. To capture this dynamic process, we construct a daily Cumulative Sentiment Index (CSI) that aggregates previously released news while allowing their impact to decay gradually.

Each news headline is evaluated using the sentiment classification model described in Section 2.3.1, which generates an individual sentiment score $s_i$. The CSI aggregates these scores across time using an event-smoothing structure. Intuitively, newly released information exerts a stronger influence on market sentiment, and its effect weakens as market attention shifts to subsequent developments.

Formally, the daily value of the cumulative sentiment index is defined as

$$CS{I}_d={\displaystyle \sum _{i }{s}_i}·e^{-\lambda (d-t_i )}$$

(6)

where the summation is taken over all news items $i$ satisfying $t_i\le d\le t_i+W$, $d$ denotes the target date, $s_i$ is the model-derived sentiment score of news item $i$, $t_i$ is its publication date, $W$ determines the length of the post-publication influence window, and $\lambda$ governs the rate at which sentiment impact decays over time. In this study, the parameters are set to $W=7$ and $\lambda =0.1$ for constructing the CSI. The sensitivity of forecasting performance to these parameter choices is examined in the subsequent analysis.

The resulting shipping news sentiment index is illustrated in Figure 2. Key event windows are highlighted, revealing pronounced sentiment fluctuations around major shocks. The index exhibits a sharp decline during the outbreak of the COVID-19 pandemic, a short-term surge surrounding the Suez Canal blockage, sustained volatility during the Red Sea crisis, and a gradual recovery during periods of policy adjustment. These patterns are consistent with the documented market impacts of these events, thereby supporting the index’s ability to sensitively capture dynamics in shipping market sentiment.

2.4. Data Decomposition and Reconstruction

To isolate the intrinsic fluctuation structure of the BDI time series, a decomposition–reconstruction framework based on variational mode decomposition (VMD) and fuzzy C-means (FCM) clustering is implemented. VMD is formulated as a constrained variational optimization problem in which the observed signal $f\left(t\right)$ is decomposed into $K$ band-limited modal components $m_k\left(t\right)$ with associated center frequencies ${\omega }_k$, satisfying the reconstruction constraint:

$$f(t)={\displaystyle \sum _{k=1}^K{m}_k}(t)+r(t)$$

(7)

where $r\left(t\right)$ denotes the residual component. The decomposition minimizes the aggregate bandwidth of all modes, defined as:

$${\min }_{\left\{m_k\right\}, \left\{{\omega }_k\right\}}{\displaystyle \sum _{k=1}^K{‖{\mathsf{\partial }}_t\left[\left(\delta (t)+\frac{j}{\pi t}\right)\ast m_k(t)\right]e^{-j{\omega }_{k}t}‖}_2^2}$$

(8)

The constrained problem is solved via an augmented Lagrangian formulation using the alternating direction method of multipliers. Modal components and center frequencies are updated iteratively as specified in Equations (9) and (10) until the convergence criterion in Equation (11) is satisfied.

$${\omega }_k^{(n+1)}={\displaystyle \frac{{\displaystyle {\int }_0^{\infty }\omega }{\left|{\widehat{m}}_k^{(n+1)}(\omega )\right|}^{2}d\omega }{{\displaystyle {\int }_0^{\infty }{\left|{\widehat{m}}_k^{(n+1)}(\omega )\right|}^2}d\omega }}$$

(9)

$${\widehat{m}}_k^{(n+1)}(\omega )={\displaystyle \frac{\widehat{f}(\omega )-{\displaystyle \sum _{i\ne k}{\widehat{m}}_i^{(n)}}(\omega )+\frac{{\widehat{\lambda }}^{(n)}(\omega )}{2}}{1+2\alpha {(\omega -{\omega }_k^{(n)})}^2}}$$

(10)

$${\displaystyle \sum _{k=1}^K\frac{{‖m_k^{(n+1)}-m_k^{(n)}‖}_2^2}{{‖m_k^{(n)}‖}_2^2}}<\epsilon$$

(11)

Following VMD, the resulting modes are aggregated using fuzzy C-means clustering. A feature set $X=\left\{x_1, x_2,\dots , x_K\right\}$ is constructed based on each mode’s center frequency, mean amplitude, and fluctuation intensity. The two key parameters, the number of clusters $c$ and the fuzziness coefficient $m$, are predefined according to standard clustering criteria. Cluster memberships and centers are obtained by minimizing the objective function:

$$J(U,V)={\displaystyle \sum _{i=1}^K{\displaystyle \sum _{j=1}^c{u}_{ij}^m}}{‖x_i-v_j‖}^2$$

(12)

The iteration terminates when the error falls below 10⁻⁵, after which modes assigned to the same cluster are superposed to obtain reconstructed modal components, yielding a parsimonious representation of the underlying dynamics.

2.5. Sequence Complexity Measurement

Following decomposition, the freight index series is represented by reconstructed modal components with heterogeneous dynamic characteristics, ranging from highly regular and quasi-deterministic patterns to irregular and strongly stochastic fluctuations. Applying a uniform forecasting strategy across all components may therefore be suboptimal. To quantify this heterogeneity, sample entropy (SampEn) is employed to measure the complexity of each reconstructed modal component and to support complexity-adaptive modeling.

For a time series $\left\{u\right(i){\}}_{i=1}^N$, vectors of embedding dimension $l$ are constructed as:

$$y(i)=\{u(i),u(i+1),\dots , u(i+l-1)\}$$

(13)

and the distance between vectors $y\left(i\right)$ and $y\left(j\right)$ is evaluated. Vector pairs with distances smaller than a tolerance $r$ are regarded as similar, and the proportion of similar pairs is defined as:

$$B_l(r)={\displaystyle \frac{1}{N-l}}{\displaystyle \sum _{i=1}^{N-l}\frac{1}{N-l-1}}{\displaystyle \sum _{j\ne i}\Theta }(r-d[y(i), y(j)])$$

(14)

where $\Theta \left(·\right)$ denotes the indicator function and $d\left(·\right)$ is the distance metric. Averaging over all vectors yields:

$$B_l(r)={\displaystyle \frac{1}{N-l}}{\displaystyle \sum _{i=1}^{N-l}{B}_l^i}(r)$$

(15)

Increasing the embedding dimension to $l+1$ and repeating the procedure gives $B_{l+1}\left(r\right)$, and sample entropy is defined as:

$$\mathit{SampEn}(l, r, N)=-\ln {\displaystyle \frac{B_{l+1}(r)}{B_l(r)}}$$

(16)

Lower SampEn values indicate stronger regularity and lower forecasting difficulty, whereas higher values reflect greater complexity and randomness.

To classify reconstructed modal components by complexity, a relative threshold is introduced to avoid scale dependence. The threshold is defined as:

$$S={\displaystyle \frac{\max (\mathit{SampEn})-\min (\mathit{SampEn})}{2}}$$

(17)

where $\max \left(\mathit{SampEn}\right)$ and $\mathrm{m}\mathrm{i}\mathrm{n}\left(\mathit{SampEn}\right)$ denote the maximum and minimum SampEn values across all reconstructed modal components. Components with SampEn exceeding $S$ are classified as high-complexity, and the remainder as low-complexity, providing a parsimonious and comparable basis for subsequent differentiated modeling.

2.6. Dual-Sentiment Gated Forecasting Model

A dual-sentiment gated forecasting model is constructed within a unified multi-step framework to evaluate the predictive contribution of sentiment information. Multi-step forecasting is implemented using an encoder–decoder architecture to generate $H$-step-ahead predictions.

The model takes two types of inputs: the low- and high-complexity component sequences and the cumulative shipping sentiment index (CSI). The two component groups are processed through separate encoding channels to capture heterogeneous dynamic patterns. A sentiment gating mechanism is introduced to modulate the encoded representations. The gating signal is constructed from a sentiment window of length $\mathrm{L}$, $\left\{CSI\left(d\right), CSI(d-1),\dots , CSI(d-L+1)\right\}$, which contains only observations up to the forecasting origin $d$. It is transformed into a weight vector in [0, 1] and applied to the encoded representations prior to decoding.

Given the pronounced non-stationarity and heavy-tailed characteristics of the BDI series, the model is trained to predict the first-order difference in BDI rather than its level. The model forecasts the first-order differences over the next $H$ horizons. Let $BDI\left(d\right)$ denote the observed level at the forecasting origin $d$. Future BDI levels are reconstructed by cumulatively summing the predicted differences and adding them to this observed initial value. All performance evaluations are conducted on the reconstructed BDI levels. Multi-step forecasting errors are evaluated in a horizon-wise manner, with RMSE, MAE, and $R^2$ computed separately for each forecasting horizon, and their arithmetic mean across horizons reported as the final performance metric.

The data are partitioned chronologically into a training-and-tuning sample (the first 80% of observations) and an independent test set (the remaining 20%). Model training and hyperparameter tuning are conducted exclusively within the first 80% under an expanding-window walk-forward scheme. In each rolling iteration, the training set consists of all historical observations available up to the current forecasting origin, while a validation subset extracted from the tail of the training window is used for early stopping. The immediately following forecasting window is used for internal performance comparison. After training is completed, the model is fitted using the entire 80% training sample and evaluated on the independent test set. In the final test period, forecasts are generated using a rolling-origin scheme with a one-step shift, where each day serves as a forecasting origin and an $H$-step-ahead sequence is produced.

The architecture, illustrated in Figure 3, implements the empirical configuration adopted in this study. The final model employs a BiGRU encoder for the low-complexity components and a BiLSTM encoder for the high-complexity components, each with 64 hidden units. The historical input window length and the forecasting horizon are both set to 14 time steps. The CSI window is first aggregated via global average pooling and then mapped to a 64-dimensional sigmoid-activated gating vector through a fully connected layer. The resulting weights are applied element-wise to the encoded representations. The decoder consists of a single-layer GRU with 128 hidden units, followed by a TimeDistributed dense layer that produces the 14-step output sequence. Model training employs a weighted mean squared error loss with exponentially decaying horizon weights and is optimized using the Adam algorithm (learning rate = 0.001, batch size = 16). Training runs for up to 50 epochs, with early stopping and ReduceLROnPlateau scheduling applied to enhance convergence and generalization.

3. Results

3.1. BDI Decomposition and Reconstruction

This section introduces the decomposition and reconstruction of the BDI time series, focusing on the extraction of multiscale features for improved forecasting.

3.1.1. BDI Decomposition Based on VMD

First, the value of K for VMD is selected by observing the center frequencies of the modes. VMD is performed on the BDI time series under different K values, and the distribution of center frequencies for each mode is examined. As shown in

Table 2. Distribution of modal center frequencies.

K	Energy	Center Frequency/Hz
2	1.78 × 103	0.0024	0.0163
3	1.77 × 103	0.0021	0.0143	0.0401
4	1.75 × 103	0.0017	0.0126	0.0257	0.0688
5	1.71 × 103	0.0014	0.0099	0.0183	0.0376	0.0782
6	1.68 × 103	0.0012	0.0077	0.0170	0.0358	0.0716	0.1460
7	1.67 × 103	0.0012	0.0074	0.0161	0.0293	0.0509	0.0791	0.1495
8	1.67 × 103	0.0011	0.0074	0.0155	0.0284	0.0472	0.0750	0.1149	0.1611
9	1.67 × 103	0.0011	0.0073	0.0153	0.0280	0.0468	0.0743	0.1109	0.1546	0.2129

, when K = 7, the modal center frequencies are close to each other, indicating over-decomposition. Therefore, K = 6 is chosen to capture the main features of the signal while avoiding redundant information.

After decomposition, six modal components ($u_{1 }-{ u}_6$) are obtained, as shown in Figure 4. The modes are ordered from low to high-frequency and from large to small amplitude, reflecting different market trends and volatility characteristics.

3.1.2. Component Reconstruction Based on FCM

First, the time-scale characteristics of the modal components are analyzed. The average period of each modal component $u_k$ is calculated using FFT, as shown in

Table 3. Temporal scale characteristics of reconstructed modal components.

Component	${\mathit{u}}_{\mathbf{1}}$	${\mathit{u}}_{\mathbf{2}}$	${\mathit{u}}_{\mathbf{3}}$	${\mathit{u}}_{\mathbf{4}}$	${\mathit{u}}_{\mathbf{5}}$	${\mathit{u}}_{\mathbf{6}}$
Average Period (Weeks)	1888.00	209.78	53.94	33.71	12.67	6.40

. Based on the time-scale similarity analysis of the BDI modal components, the clustering number is set to 4.

Multiple runs of the FCM algorithm yield stable and consistent clustering results. The reconstructed modal components are reconstructed into trend, low-frequency, mid-frequency, and high-frequency components, labeled as $y_{1 }$ to $y_4$, where $y_1$ corresponds to $u_1$, $y_2$ to $u_2$, $y_3$ to $u_3$, and $y_4$ aggregates $u_4$ to $u_6$. These components are compared with the original BDI series, as illustrated in Figure 5, forming the basis for subsequent complexity analysis and forecasting.

3.1.3. Economic Interpretation of the Reconstructed Modal Components

This section analyzes the economic significance of the reconstructed components using the average period, variance contribution, and Pearson correlation with the BDI. The average period, computed via FFT, reveals the primary fluctuation cycle. Variance contribution reflects the explanatory power of each component for BDI fluctuations, calculated as the ratio of each component’s variance to the total variance. The Pearson correlation coefficient quantifies the linear relationship between each component and the BDI. The results are shown in

Table 4. Statistical analysis of the reconstructed modal components.

Component	${\mathit{y}}_{\mathbf{1}}$	${\mathit{y}}_{\mathbf{2}}$	${\mathit{y}}_{\mathbf{3}}$	${\mathit{y}}_{\mathbf{4}}$
Average Period (Weeks)	944.00	89.90	52.44	17.48
Variance Contribution (%)	84.32%	6.62%	1.36%	0.25%
Pearson Correlation Coefficient	0.9481	0.3731	0.2139	0.0874

.

The statistical analysis shows distinct differences among the trend, low-frequency, mid-frequency, and high-frequency components, reflecting their diverse volatility characteristics and economic roles.

Trend Component ($y_1$): Dominated by long-term supply–demand structural factors. The trend component exhibits the longest period and the highest variance contribution, indicating it primarily captures the long-term trend of the BDI. It is highly correlated with the BDI and reflects deep structural changes in the global shipping market, such as fleet expansion, global economic shifts, and long-term trade adjustments. This component shows slow, directional fluctuations and constitutes the core of the BDI’s long-term trend.

Low-Frequency Component ($y_2$): Reflecting structural shocks in specific phases. The low-frequency component has a relatively long period and moderate volatility, representing market responses to significant events, such as policy changes, geopolitical shifts, or macroeconomic disruptions. While the impacts are generally not sustained, they can cause significant price deviations over specific periods. This component captures non-trend fluctuations during structural adjustments in the BDI.

Mid-Frequency Component ($y_3$): Manifesting seasonal patterns and cyclical economic activities. The mid-frequency component exhibits typical cyclical characteristics, mainly related to demand fluctuations driven by seasonal changes or production cycles in the shipping market, such as agricultural transport seasons or peaks around holidays. These fluctuations are often predictable, repeating annually, and are inherent to the transport market’s seasonal dynamics.

High-Frequency Component ($y_4$): Reflecting short-term disturbances and market noise. The high-frequency component has the shortest period and most intense fluctuations, displaying significant short-term jumps and irregularities. Its sources may include temporary policy changes, fuel price fluctuations, currency variations, or sudden market sentiment shifts. This component reflects market sensitivity to immediate, sporadic information and represents typical short-cycle disturbances.

3.1.4. Complexity Evaluation of Modal Components

The complexity of the four BDI modal components is assessed using sample entropy, as shown in

Table 5. Sample entropy and complexity evaluation of each modal components.

Component	Sample Entropy	Complexity Classification
$y_{1 }$	0.0135	Low-Complexity
$y_2$	0.0667	Low-Complexity
$y_3$	0.3155	High-Complexity
$y_{4 }$	0.4868	High-Complexity
Threshold S	0.2366	—

.

The sample entropy values of $y_1$ and $y_2$ are below the threshold $S$, indicating strong regularity and low randomness, thus classified as low-complexity modes. These components generally reflect stable trends or periodicity, suitable for linear forecasting models. In contrast, $y_3$ and $y_4$ show higher sample entropy values, signifying more complex, irregular structures and classifying them as high-complexity modes. These components, with larger fluctuations, are better modeled by nonlinear methods like neural networks or ensemble learning.

Overall, the sample entropy confirms the effectiveness of VMD: lower-order components ($y_1$, $y_2$) are more regular, while higher-order components ($y_3,$ $y_4$) exhibit greater randomness. Based on these evaluations, differentiated forecasting models will be applied to low- and high-complexity modes to improve the accuracy and robustness of the forecast.

3.2. Forecasting Performance Evaluation

The forecasting performance of the proposed framework is evaluated on the independent test set defined in Section 2.6. All error metrics are computed on reconstructed BDI levels in their original scale. Multi-step forecasting accuracy is assessed in a horizon-wise manner, with RMSE, MAE, and $R^2$ calculated separately for each forecasting horizon and averaged across horizons to obtain the final performance measure.

3.2.1. Sentiment Integration Strategies

To assess the impact of the sentiment gating mechanism versus traditional input methods, three sentiment handling approaches are used: direct input of sentiment indices, sentiment indices lagged by 14 periods, and a weighted lagged sentiment index based on Granger causality test results. The direct input method incorporates the sentiment index alongside other modal components into model training for automatic learning of their relationships. The lagged 14-period input method, based on the lag effect from Granger causality tests, captures the short-term delayed impact of sentiment on the BDI. The weighted lagged sentiment method determines specific lags for each modal component ($y_1$: 1, 3, 5 lags; $y_3$: 1 lag; $y_4$: 14, 17, 21 lags) and assigns differentiated weights to the lagged sentiment indices according to the test p-values.

As shown in

Table 6. Performance comparison of different sentiment integration strategies.

Model	RMSE	MAE	R2
Benchmark Model	87.92	61.47	0.9238
Dual-Sentiment Gated Model	66.83	45.51	0.9535
Direct Sentiment Input	77.67	65.06	0.9041
Lagged 14-Period Sentiment Input	96.15	75.92	0.8827
Weighted Lagged Sentiment Input	74.81	60.65	0.9372

, the dual-sentiment gated model performs best in both error and fit measures. It significantly outperforms the benchmark model without sentiment and surpasses all sentiment input models, demonstrating the effectiveness of the gating mechanism. This approach avoids the complexity of lag selection and weight calculation, dynamically adjusting sentiment weights and adapting to the complex relationship between sentiment and the BDI, thereby greatly improving prediction accuracy. In contrast, the direct input of sentiment indices and lagged 14-period input fail to capture the deep relationship between sentiment and BDI, leading to moderate performance. Even the weighted lagged method, which matches exclusive lags and assigns differential weights to capture multi-phase sentiment effects, does not perform as well as the gating model.

3.2.2. Forecasting Architectures

The forecasting performance of different neural architectures, including RNN, BiGRU, and BiLSTM, is compared under a fixed forecasting horizon using the proposed dual-gating mechanism with sentiment integration. To ensure comparability, models are evaluated under consistent training conditions, with hyperparameter settings held constant except for architecture-specific adjustments. The comparative performance results are reported in

Table 7. Performance comparison of different forecasting models based on dual-gating mechanism.

Model	Dual-Gating Mechanism			Without Sentiment Index
	RMSE	MAE	R2	RMSE	MAE	R2
RNN	224.18	198.64	0.7478	247.45	218.36	0.7117
BiGRU	79.58	68.76	0.9341	97.66	73.59	0.8932
BiLSTM	136.72	116.41	0.8195	158.48	127.39	0.7975
Low RNN, High BiGRU	99.10	82.68	0.8802	112.35	75.59	0.8344
Low RNN, High BiLSTM	92.71	67.99	0.9079	108.18	83.72	0.8763
Low BiGRU, High BiLSTM	66.83	45.51	0.9535	87.92	61.47	0.9138

.

Across single-encoder architectures, bidirectional recurrent models outperform the basic RNN structure, indicating that capturing both forward and backward temporal dependencies is beneficial for BDI forecasting. When examining hybrid configurations, models that assign BiGRU to low-complexity components and BiLSTM to high-complexity components achieve superior overall performance. This pattern suggests that low-complexity components, which typically exhibit smoother and more persistent dynamics, are effectively modeled by the relatively parameter-efficient BiGRU structure. In contrast, high-complexity components contain stronger volatility and irregular fluctuations, and the memory capacity of BiLSTM appears better suited to capturing such nonlinear and longer-range variations. These results are consistent with the heterogeneous nature of the decomposed BDI structure.

Overall, incorporating sentiment through the dual-gating mechanism improves forecasting performance across all examined architectures. The consistent advantage of sentiment-gated variants over their no-sentiment counterparts indicates that sentiment modulation provides complementary information beyond structural time-series patterns. Together, complexity-aware modeling and sentiment integration contribute to more stable and accurate multi-step BDI forecasts.

3.2.3. Forecasting Horizons

To assess the effectiveness of the sentiment gating mechanism across different time spans, the model’s performance is compared for forecasting horizons of 1, 7, 14, and 21 days, as shown in

Table 8. Performance comparison across different forecasting horizons.

Forecast Horizon	Dual-Gating Mechanism			Without Sentiment Index
	RMSE	MAE	R2	RMSE	MAE	R2
1	36.94	25.57	0.9876	45.76	33.16	0.9713
7	54.27	37.69	0.9679	71.54	53.72	0.9463
14	66.83	45.51	0.9535	87.92	61.47	0.9138
21	83.45	63.12	0.9264	99.73	76.30	0.8735

.

As the forecast horizon extends, the model’s performance gradually declines, but the metrics remain within acceptable thresholds, reflecting consistent and dependable performance. This indicates that while accuracy diminishes over time, the 14-day forecasting window continues to provide stable and valuable predictions, suggesting its practical applicability. The sentiment index also shows an increasingly significant effect on prediction accuracy as the horizon lengthens, underscoring the model’s ability to effectively incorporate sentiment information. Overall, the model demonstrates robustness in multi-step forecasting, offering reliable predictions within reasonable timeframes.

3.3. Sensitivity Analysis of CSI Parameters

To evaluate the robustness of the CSI construction, a sensitivity analysis was conducted on the two key parameters: the event window length $\mathrm{W}$ and the decay parameter $\mathsf{\lambda }$. These parameters jointly determine the duration and attenuation of news influence in the sentiment index. The forecasting performance under different parameter combinations is reported in

Table 9. Forecasting performance under different CSI parameter settings.

$\mathbf{W}$	$\mathsf{\lambda }$	Dual-Gating Mechanism			Without Sentiment Index
		RMSE	MAE	R2	RMSE	MAE	R2
3	0.05	70.58	48.23	0.9481	94.67	66.91	0.9012
	0.1	69.14	46.97	0.9503	91.45	64.28	0.9075
	0.2	73.42	51.08	0.9438	96.33	68.75	0.8956
7	0.05	68.79	47.22	0.9510	89.94	63.12	0.9102
	0.1	66.83	45.51	0.9535	87.92	61.47	0.9138
	0.2	67.91	46.38	0.9522	90.28	63.55	0.9089
14	0.05	70.25	48.67	0.9476	93.56	65.89	0.9034
	0.1	68.07	46.55	0.9518	89.15	62.43	0.9117
	0.2	69.48	47.79	0.9490	91.02	64.17	0.9063

.

The results indicate that forecasting performance remains broadly stable across different parameter combinations. The benchmark specification $W=7$ and $\lambda =0.1$ generally provides competitive or slightly better performance than alternative settings. This pattern reflects the exponential decay mechanism in the CSI construction, which progressively reduces the influence of older news and aligns the effective sentiment signal with the pace at which market expectations adjust in the shipping industry. Overall, the results indicate that moderate variations in the CSI parameters do not materially alter the forecasting outcomes, supporting the robustness of the proposed forecasting framework.

4. Case-Based Discussion

To better understand the mechanisms underlying the observed performance gains, it is informative to examine the model’s behavior during a period of abrupt exogenous shock. The Red Sea crisis in late 2023 constituted a sudden exogenous shock to the global dry bulk shipping market, marked by severe security risks, forced vessel rerouting around the Cape of Good Hope, and an abrupt contraction in effective transport capacity. Such conditions led to heightened uncertainty and rapidly deteriorating market expectations, creating a setting in which freight rate dynamics departed sharply from historical patterns. During this period, shipping-related news coverage intensified and was accompanied by a pronounced decline in the sentiment index, reflecting a rapid reassessment of market conditions by industry participants.

Starting from the outbreak of the crisis on 19 October 2023, multi-step forecasts generated by the proposed model exhibit close alignment with observed BDI movements, as illustrated in Figure 6. The model successfully captures both the downward trend and the increased volatility observed in the early stage of the disruption. Compared with approaches that rely exclusively on past freight rates, the inclusion of sentiment information improves responsiveness to abrupt market deterioration, suggesting that textual sentiment contains forward-looking signals that precede their full incorporation into price-based indicators.

The empirical behavior observed during the crisis highlights the functional role of the sentiment gating mechanism. Under conditions of structural disruption, historical freight dynamics provide limited guidance due to rapid shifts in supply–demand balance and elevated uncertainty. By dynamically modulating the influence of sentiment signals, the gating mechanism allows negative sentiment to exert stronger influence on high-complexity components, which are more sensitive to irregular shocks and short-term disturbances. This adaptive adjustment mitigates the risk of mechanical trend extrapolation and enhances the model’s ability to accommodate regime changes.

Beyond its methodological implications, the Red Sea crisis also illustrates how sentiment-enhanced forecasting models can inform decision-making under extreme market stress. In this context, the model consistently signaled downward pressure on the BDI, providing early indications of deteriorating market conditions. From a short-term perspective, such signals may assist shipping firms in evaluating tactical responses aimed at mitigating immediate operational risks, including reassessing routing options, strengthening customer communication, and improving cost control through more flexible capacity scheduling and fuel management. From a medium- to long-term perspective, the persistence of negative sentiment and sustained market stress suggests the need for more strategic adjustments if disruptions to key shipping lanes are expected to continue; sentiment-informed forecasts may therefore support decisions related to capacity restructuring, long-term contract negotiation, and strategic repositioning under multiple contingency scenarios. Rather than prescribing specific actions, these results demonstrate how timely anticipation of adverse freight dynamics can enhance both operational preparedness and longer-horizon strategic alignment under abrupt and recurring disruptions.

5. Conclusions

This study proposes a complexity-aware and sentiment-integrated forecasting framework for the Baltic Dry Index (BDI) by combining shipping news sentiment with multiscale time-series modeling. The empirical results show that the proposed model significantly outperforms benchmark methods, especially under extreme market conditions, where the integration of sentiment information enhances the robustness of the predictions. These findings highlight the importance of incorporating market sentiment into freight rate forecasting frameworks, which helps achieve more resilient predictions and risk-aware decision-making in volatile shipping markets.

However, there are some limitations in this study. The granularity of sentiment classification could be refined, with future research exploring more detailed sentiment categories. While the current model performs well, exploring diverse forecasting models and optimization strategies could further improve accuracy and adaptability. Lastly, sentiment data application remains limited, and future work could extend the framework to multi-market settings to study how sentiment shocks propagate across shipping, commodity, and energy markets, especially under extreme conditions. This would provide new insights for cross-market risk assessment and decision-making.