Comparative Evaluation of Deep Learning Model Complexity for Forecasting Non-Ferrous Metal Prices

Summary

A systematic reevaluation of 13 architectures for metal price forecasting shows that a simple gated recurrent unit outperforms more complex hybrid models. Models trained on copper and tested on aluminum and zinc demonstrate consistently high predictive accuracy, supporting the use of parsimonious approaches in commodity price forecasting.

Abstract

This study examines whether increasing architectural complexity improves forecasting accuracy in deep learning–based financial models. Using daily spot price data from the Shanghai Metals Market for copper (Cu), aluminum (Al), and zinc (Zn) spanning January 2015 to September 2025, a standardized preprocessing pipeline was applied, including z-score normalization and sliding window sequence construction (window length = 30, forecast horizon = 1). A total of eighteen models were systematically evaluated, including gated recurrent units (GRUs), long short-term memory (LSTM) networks, convolutional neural network–bidirectional LSTM–attention hybrids (CNN–BiLSTM–Attention), as well as traditional econometric models (autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity), machine learning models (random forest and extreme gradient boosting), and a Transformer-based model. All deep learning models were trained exclusively on Cu data and evaluated on independent Al and Zn datasets to assess generalizability. Results show that the standard GRU model achieves the lowest error rates (mean absolute error [MAE] = 1032.85; root mean square error = 1344.30) and highest explanatory power (coefficient of determination [R²] = 0.907) on the Cu test set, while also performing strongly on Al (MAE = 167.51, R² = 0.918) and Zn (MAE = 254.23, R² = 0.952). Ablation analysis demonstrates that adding architectural components such as attention mechanisms, bidirectional layers, and convolutional modules reduces predictive accuracy. Statistical testing using the Diebold–Mariano test indicates that most performance differences are significant (p < 0.05). These findings highlight the limitations of unnecessary model complexity and support the use of simpler, robust approaches for commodity price forecasting.

Introduction

The global non-ferrous metals market—encompassing copper (Cu), aluminum (Al), and zinc (Zn)—is a linchpin of the world economy. These metals are fundamental to construction, manufacturing, transportation, and the rapidly expanding green energy infrastructure^1,2. Consequently, their price dynamics are characterized by high volatility, driven by a complex interplay of macroeconomic forces, geopolitical tensions, supply chain disruptions, speculative financial activities, and linkages to energy markets^3,4. Accurate forecasting is not merely academic but a pressing practical necessity for governments (strategic resource security), mining corporations (production planning), industrial consumers (procurement), and financial institutions (risk management and trading)^5,6.

The quest for predictive accuracy has propelled methodological evolution. Traditional econometric approaches—autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models—have long been applied to capture linear dependencies and volatility clustering^7,8. However, they often struggle with non-linear, non-stationary, and high-frequency noise⁹. Machine learning (ML) techniques, such as support vector machines and random forests, offered a leap forward by modeling complex non-linear relationships without stringent distributional assumptions^10,11. Yet, their capacity to capture long-range temporal dependencies remains constrained. The true paradigm shift arrived with deep learning (DL)¹², particularly recurrent neural networks (RNNs). Long short-term memory (LSTM) networks¹³ and their streamlined variant, the gated recurrent unit (GRU)^14,15, effectively mitigate the vanishing gradient problem and have become de facto standards for financial time series forecasting, including metal price prediction^16,17,18,19. Numerous studies have applied these DL methods to non-ferrous metal markets, demonstrating improved accuracy over classical benchmarks^{20,21,22,23,24,25,26,27}.

Subsequent research, however, has largely pursued increasing architectural complexity, driven by innovations in other artificial intelligence (AI) domains. This trajectory can be categorized into three synergistic trends. First, hybridization with one-dimensional convolutional neural networks (CNNs) to extract local multiscale features before temporal modeling (e.g., CNN–LSTM or CNN–GRU)^28,29,30. Second, bidirectional processing (bidirectional LSTM [BiLSTM] and bidirectional GRU [BiGRU]), which processes sequences forwards and backwards to capture richer contextual information^31,32. Third, the incorporation of attention mechanisms, which allow models to dynamically weigh the importance of historical time steps^33,34. The logical culmination is multicomponent “super-hybrids” such as CNN–BiLSTM–Attention or CNN–BiGRU–Attention^35,36. A pervasive, often implicit assumption underpinning much of this research is that architectural complexity is synonymous with improved forecasting accuracy, leading to a “complexity arms race” in AI-driven financial literature³⁷.

This assumption warrants critical scrutiny. Increased model complexity carries significant costs: a drastic expansion in trainable parameters, heightened risk of overfitting—especially on finite, noisy financial datasets—greater computational resource requirements, longer training times, and reduced interpretability^38,39. Emerging critiques have begun to report diminishing returns or even performance degradation when overly complex models are applied to noisy, medium-sized datasets^40,41. The attention mechanism, while powerful in domains such as natural language processing with clear semantic structures, may struggle to learn meaningful weighting schemes in chaotic price series, potentially learning spurious correlations or failing to converge⁴². Despite these concerns, a systematic, head-to-head empirical evaluation of the complexity–performance trade-off specifically in multimetal price forecasting has been conspicuously absent from the literature.

Recent studies have advanced commodity price forecasting using various deep learning approaches. A motif-based graph representation learning approach was proposed to analyze transaction graphs for cryptocurrency price prediction⁴³. Graph neural network-based temporal deep learning models were developed for financial asset price prediction⁴⁴. Time-series deep learning models were applied to pairs trading in financial markets⁴⁵. Hypergraph neural networks were used to capture higher-order relationships among stocks for predicting stock movements⁴⁶. Collectively, these works underscore the growing interest in model selection but do not systematically compare simple architectures against a full spectrum of complex hybrids under identical experimental conditions—a gap this study addresses.

We also acknowledge recent Transformer-based time series models (e.g., Informer, Autoformer, Temporal Fusion Transformer, and PatchTST). These models have shown promise in long-sequence forecasting but typically require extensive data. In our preliminary experiments, a standard Transformer (encoder only) trained on the same dataset (2,602 daily observations, window = 30) performed poorly, achieving negative R² values on all three metals. This outcome is consistent with the view that Transformers are data intensive and may not be suitable for data-limited commodity market scenarios. Given our focus on a realistic, medium-frequency forecasting environment, we exclude advanced Transformer variants from the main benchmark, while noting that testing them on larger datasets remains an important future direction.

This study directly addresses the identified gaps by rigorously testing the hypothesis that simpler deep learning architectures can outperform their more complex counterparts in forecasting daily prices of Cu, Al, and Zn. We design and implement a comprehensive benchmarking framework encompassing thirteen state-of-the-art models—ranging from the foundational GRU and LSTM to advanced hybrid architectures such as CNN–BiGRU–Attention and CNN–BiLSTM–Attention. Our analysis is anchored on a substantial dataset from the Shanghai Metals Market (SMM) spanning January 2015 to September 2025. Crucially, all models are trained exclusively on Cu price data, while Al and Zn datasets are reserved strictly for independent out-of-sample validation to test generalizability. We also conduct structured ablation experiments to isolate and quantify the individual and combined impact of adding attention mechanisms, bidirectional layers, and convolutional modules to baseline recurrent models, thereby directly interrogating the value of each component of complexity.

The contributions of this work are threefold. First, it provides a comprehensive empirical benchmark for deep learning-based metal price forecasting, offering a clear, evidence-based hierarchy of model performance. Second, it delivers a substantive critical intervention in the field, challenging the unquestioned pursuit of architectural complexity and highlighting the significant risks of overfitting and inefficiency. Third, it offers pragmatic guidance to researchers, analysts, and industry practitioners, advocating for a principle of parsimony: simpler, well-tuned models such as the GRU may be not only sufficient but superior for certain financial forecasting tasks, offering a favorable balance of accuracy, speed, robustness, and transparency. The remainder of this paper is structured as follows. The Protocol section details the research methodology, including data, preprocessing, model architectures, training protocols, and evaluation metrics. The Results section presents the empirical results, including primary benchmarking, ablation studies, and generalizability tests. The Discussion section discusses the theoretical and practical implications, limitations, and future directions.

Protocol

This study did not involve human participants or vertebrate animal subjects. All data used are publicly available commodity price series from the SMM, which do not require ethical approval. Therefore, no ethical approval was sought or required for this research.

This section delineates the comprehensive and rigorous research design implemented to empirically test the core hypothesis. It provides a detailed exposition of the mathematical formulation and architectural specifics of the thirteen evaluated deep learning models, the precise training protocol, and the formal evaluation metrics. The overarching methodological workflow is visually summarized in Figure 1.

Figure 1: Schematic overview of the research methodology. The diagram illustrates the complete experimental pipeline, including data partitioning, model training exclusively on the Cu price series, evaluation on the Cu test set, and out-of-sample validation on independent Al and Zn series. The dashed feedback loop indicates the structured ablation experiments conducted to analyze the contribution of individual architectural components. Please click here to view a larger version of this figure.

The diagram illustrates the complete experimental pipeline. The process begins with the exclusive use of the Cu price series for model development. This series is partitioned chronologically into training (80%), validation (10%), and test (10%) sets. Thirteen distinct deep learning architectures are then trained and hyperparameter-optimized solely on the Cu training data, with early stopping monitored via the validation set. The primary benchmark is the evaluation of these models on the held-out Cu test set. Crucially, to assess generalizability, the exact same trained models are applied without modification to forecast the entirely independent Al and Zn price series, representing a strict out-of-sample test. Finally, structured ablation experiments (the dashed feedback loop) are conducted to decompose and analyze the performance contribution of individual architectural components (e.g., attention, bidirectional processing, and convolutional layers).

Model Architectures and Mathematical Formulation
We designed and implemented a spectrum of 13 DL models, systematically increasing in architectural complexity from simple recurrent networks to sophisticated multicomponent hybrids. All models share the same core objective: to learn a mapping  from a historical price window X_t = [P_t-L,P_t-L+1,…,P_t-1] of length L = 30 to the subsequent price y_t = P_t.

The model families are defined as follows:

Baseline Recurrent Models
GRU: A streamlined recurrent network employing update (z_t) and reset (r_t) gates to modulate information flow. The hidden state h_t is computed as:

   (1)

   (2)

  (3)

    (4)

where X is the sigmoid activation,  denotes the Hadamard product, and x_t is the input at time t . The final hidden state h_L is passed through a linear output layer. Equations 1–4 are adapted from Cho et al.¹⁴.

LSTM: Utilizes input (i_t), forget (f_t), and output (o_t) gates to maintain a cell state (C_t), providing more explicit control over long-term memory.

Bidirectional Models (BiGRU and BiLSTM)
These models incorporate two separate recurrent layers that process the sequence in forward and reverse directions. The final hidden representation at each time step is the concatenation , theoretically capturing contextual information from both past and future within the fixed input window.

Attention-Augmented Models (GRU–Attention and LSTM–Attention)
An additive attention mechanism is applied to the sequence of hidden states H = [h₁,h₂,…,h_L] produced by the final recurrent layer. The context vector is defined as a weighted sum:

(5)

(6)

(7)

Here, α_i represents the attention weight assigned to the i-th historical time step. The context vector c, encapsulating an adaptive summary of relevant history, is fed to the final prediction layer. Equations 5–7 are adapted from Bello et al.⁴⁷.

CNN–Hybrid Models (CNN–GRU and CNN–LSTM)
A one-dimensional CNN layer with rectified linear unit (ReLU) activation is prepended to the recurrent layer.

Complex Hybrid Models
These architectures combine multiple components (e.g., CNN–BiGRU–Attention, CNN–BiLSTM–Attention). They represent the state of the art in terms of complexity, aiming to integrate local pattern extraction (CNN), bidirectional contextual modeling, and adaptive temporal weighting (attention) into a single framework.

All models were configured with consistent hidden state dimensions (128 units for recurrent layers and 64 filters for CNN layers) and were finalized with a single linear output layer. This controlled design ensures that performance differences are attributable to architectural choices rather than discrepancies in model capacity tuning. The number of trainable parameters consequently increased substantially along this spectrum.

Training Protocol, Hyperparameters, and Ablation Study Design
Table 1 summarizes the unified and rigorous experimental configuration applied to all thirteen models to ensure a fair comparison and mitigate overfitting. All models were trained from scratch using only the designated Cu training set. The Adam optimizer was used to minimize the mean squared error (MSE) loss. The critical technique of early stopping, monitored on the Cu validation set, was uniformly applied. This ensured that training concluded at the point of optimal generalization on unseen Cu data, thereby preventing models from overfitting to training noise.

Parameter Category	Specification / Value	Description
Core Task & Data
Forecasting Target	Next-day price	Standard one-step-ahead prediction.
Input Window Length (L)	60 trading days	Balances sufficient historical context with model complexity and training stability.
Model Development
Training Set (Cu-only)	First 80% (~2081 observations)	Used for learning model parameters via backpropagation.
Validation Set (Cu-only)	Next 10% (~260 observations)	Used for hyperparameter tuning and early stopping; crucial for preventing overfitting.
Test Set (Cu-only)	Final 10% (~260 observations)	Final, held-out evaluation of in-sample (Cu) performance.
Model Architecture
RNN Hidden Units	128	Provides adequate representational capacity; kept constant across all RNN-based models.
CNN Filters	64	Number of feature maps for CNN layers in hybrid models.
Training Procedure
Optimizer	Adam	Adaptive learning rate optimizer for stable and efficient convergence.
Initial Learning Rate	1 × 10⁻³	Standard starting rate for Adam.
Loss Function	Mean squared error (MSE)	Standard for regression
Batch Size	32	Efficient mini-batch training.
Maximum Epochs	80	Upper limit for training iterations.
Early Stopping Patience	10 epochs	Training halts if validation loss does not improve for 20 consecutive epochs; model weights from the best epoch are restored.
Evaluation & Validation
Primary Metrics	MAE, RMSE, R²	Provide complementary views of error magnitude and variance explained.
Generalizability Test	Forecast on full Al and Zn series (2602 observations each)	Models are frozen after Cu training. This is a pure, strict out-of-sample test on entirely different commodities.
Ablation Design	GRU → BiGRU → BiGRU–Attention → CNN–BiGRU–Attention	Systematically isolates the impact of adding bidirectionality, attention, and CNN components.

Table 1: Key experimental parameters and configuration. Summary of the experimental setup applied across all models, including data partitioning, model architecture parameters, training settings, and evaluation metrics.

To deconstruct the contribution of each architectural component, a structured ablation study was designed. Starting from the best-performing baseline (GRU), a progressive “complexity chain” was constructed. Figure 2 visually outlines this complexity chain, illustrating the stepwise addition of components. This stepwise approach allows for the direct attribution of any change in forecasting performance to the incremental addition of bidirectionality, the attention mechanism, and finally the convolutional neural network layer. The performance metrics at each node of this chain provide clear empirical evidence on the value or detriment of each complexity component for the specific task of metal price forecasting.

Figure 2: Complexity chain used in the ablation study. The diagram illustrates the stepwise addition of architectural components, progressing from GRU to BiGRU, BiGRU–Attention, and CNN–BiGRU–Attention. This sequence represents the systematic increase in model complexity used to evaluate the impact of each component on forecasting performance. Please click here to view a larger version of this figure.

Performance Evaluation Metrics
Model performance was rigorously quantified using three standard regression metrics, offering complementary insights into prediction accuracy and explanatory power.

Mean Absolute Error (MAE)
Measures the average magnitude of errors, providing a robust and easily interpretable scale of deviation.

(8)

Root Mean Square Error (RMSE)
Emphasizes larger errors due to the squaring operation, making it more sensitive to outliers and large mistakes.

(9)

Coefficient of Determination (R²)
Represents the proportion of variance in the target variable that is predictable from the model.

 (10)

where is the mean of the true values. An R² value closer to 1 indicates a model that explains most of the variance in the data. Equations 8–10 are standard regression metrics⁴⁸. The evaluation was conducted in two distinct, sequential phases to separately assess in-sample benchmark performance and out-of-sample generalizability. (1) Phase 1 (Primary Benchmark): All thirteen models, after training and early stopping on Cu data, were evaluated on the held-out Cu test set. (2) Phase 2 (Generalizability Test): The exact same models, with their parameters frozen, were deployed to generate forecasts for the complete, independent price series of Al and Zn. No retraining or adaptation was performed.

Reproducibility: Detailed Experimental Settings
Daily spot prices (CNY/ton) for Grade A Cu, Al, and Zn were obtained from the SMM public platform (https://www.smm.cn/), spanning January 5, 2015, to September 12, 2025. The raw and processed data are available in a public repository (DOI: 10.5281/zenodo.19976985). The data file contains the columns date, Cu, Al, and Zn. Dates are converted to datetime format and sorted in ascending order. Missing values are handled by forward fill followed by backward fill. Features are standardized using a z-score scaler fitted only on the training set (mean μ_j, standard deviation σ_j , ); the same and are applied to the validation and test sets without refitting. The target variable (Cu, Al, or Zn) is scaled separately using its own respective training set statistics.

Input–output sequences are constructed using a sliding window with input length L = 30 trading days and forecast horizon h = 1 (next-day prediction). For a target index (0 = Cu, 1 = Al, 2 = Zn), each sample is defined as X_i = V[ t - L : t, : ] (shape 30 × 3) and y_i = V[ t + h , k]  (scalar). No shuffling is applied to preserve temporal order. The dataset is split chronologically without randomness: training comprises indices 0–2080 (2,081 observations, 80%), validation indices 2081–2340 (260 observations, 10%), and test indices 2341–2601 (261 observations, 10%). The corresponding date boundaries are January 5, 2015, to July 31, 2023 (training), August 1, 2023, to October 19, 2023 (validation), and October 20, 2023, to September 12, 2025 (test); the file in the repository provides exact details.

Random seeds are fixed as follows: main experiment seed = 42, and Python, NumPy, and TensorFlow seeds are all set to 42. Weight initialization uses Glorot uniform for input kernels, orthogonal for recurrent kernels, and zeros for biases. The software environment consists of Python 3.10.19, TensorFlow 2.20.0/Keras, NumPy 1.26.4, pandas 2.3.3, scikit-learn 1.7.2, and Matplotlib 3.10.6. Experiments were run on a Windows 11 PC with an Intel Core i7 (2.20 GHz) and 32 GB RAM; no GPU was used.

The Adam optimizer is employed with learning_rate = 1×10^-3, β₁ = 0.9, β₂ = 0.999, , and weight_decay = 0. The loss function is MSE. A ReduceLROnPlateau scheduler monitors validation loss with factor 0.5, patience 5, and minimum learning rate 1 × 10^-5. Early stopping is applied with monitor = val_loss, patience = 10, restore_best_weights = True, and min_delta = 0. Each training epoch consists of a forward pass on the training batch, MSE loss computation, backpropagation, and Adam parameter update. After every epoch, validation loss is computed; early stopping and learning rate reduction are triggered based on this value. The model with the lowest validation loss is restored for testing. Batch size is 32, and samples are fed in chronological order without shuffling (shuffle = False).

For CNN hybrid models, one Conv1D layer with 64 filters, kernel_size = 3, stride = 1, padding = 'same', and rectified linear unit (ReLU) activation is used, followed by MaxPooling1D(pool_size = 2) and Dropout(0.15). In attention-augmented models, the recurrent neural network returns the full hidden sequence H with shape B × T × C.  A dense layer with one unit produces a score, and a softmax over time converts these scores into attention weights , with the context vector defined as c = ∑_t α_t h_t. This is followed by a dense layer with 64 units and ReLU activation, Dropout(0.15), and the output dense layer. Bidirectional models concatenate forward and backward hidden states (each 64 units), resulting in 128 dimensions; when attention is used, return_sequences = True preserves the full sequence (B × T × 128).

Evaluation uses direct one-step-ahead prediction (non-recursive). All predictions are inverse-transformed to the original price scale before computing MAE, RMSE, and R² on that scale. For generalizability tests on Al and Zn, the input scaler fitted on Cu is reused without modification, while each target metal has its own target scaler fitted on its own training targets. In the ablation study, all non-architectural parameters (data, split, scaling, random seed, number of epochs, batch size, optimizer, learning rate, loss function, early stopping, scheduler, dropout) are kept identical across the chain; only the architecture changes. The complete source code and replication instructions are publicly available at Zenodo (10.5281/zenodo.19976985). All figures were generated using Matplotlib 3.10.6 with the provided script; outputs are saved as PDF, SVG, and high-resolution PNG (600 dpi). All models were trained with a maximum of 80 epochs. Early stopping with patience = 10 (monitored on validation loss) was triggered for every model before reaching the epoch limit. For instance, the GRU model stopped at epoch 37 (best epoch 27, best validation loss 0.0040), while the most complex hybrid CNN–BiLSTM–Attention stopped at epoch 23 (best epoch 13, best validation loss 0.0072). The complete list of stopped epochs, best epochs, and best validation losses for all 13 models is available in the Zenodo repository, ensuring full transparency and reproducibility without overloading the main text with a table. The theoretical discussions (Lipschitz bounds, sample complexity, Rademacher complexity, bias–variance decomposition, attention entropy, and mutual information) are conceptual explanations for the empirical results and do not alter the training objective or model implementation. Finally, to assess stability, the main experiments were repeated with five random seeds (1, 7, 21, 42, and 2024); the mean and standard deviation of RMSE across these runs are reported in the Results section, where the GRU maintained competitive mean RMSE with low variance, supporting stable performance across random initializations.

Results

qThis section presents a comprehensive empirical evaluation of the 13 DL models and additional baseline models, following the rigorous methodology outlined in Section 3. The analysis is structured in four parts: (1) a descriptive overview of the dataset, (2) a primary benchmarking of model performance on the held-out Cu test set, including visual diagnostics of fitting and training dynamics, (3) a detailed ablation study to deconstruct the effect of architectural complexity, and (4) a critical test of model generalizabil...

Discussion

The empirical results presented in the Results section provide a clear and consistent answer to our central research question: for daily non-ferrous metal price forecasting under a realistic, data-limited regime (2,602 observations, univariate inputs, one-step-ahead horizon), the simplest deep learning architecture—the GRU—consistently and significantly outperforms a wide range of more complex models. These include hybrid CNNs, bidirectional RNNs, attention-augmented networks, and multicompon...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Dataset	Daily copper (Cu) spot price series – One of the three target metals; also part of multivariate input features.	Shanghai Metals Market (SMM), publicly available	SMM price data; column = Cu; price type = spot; frequency = daily; unit = CNY/ton; date range = 2015-01-05 to 2025-09-12; RRID: not applicable
Dataset	Daily aluminum (Al) spot price series – One of the three target metals; also part of multivariate input features.	Shanghai Metals Market (SMM), publicly available	SMM price data; column = Al; price type = spot; frequency = daily; unit = CNY/ton; date range = 2015-01-05 to 2025-09-12; RRID: not applicable
Dataset	Daily zinc (Zn) spot price series – One of the three target metals; also part of multivariate input features.	Shanghai Metals Market (SMM), publicly available	SMM price data; column = Zn; price type = spot; frequency = daily; unit = CNY/ton; date range = 2015-01-05 to 2025-09-12; RRID: not applicable
Dataset	Preprocessed multivariate metal price dataset – Chronologically sorted and cleaned Cu, Al, Zn series after missing-value handling and sliding-window construction (L = 30, h = 1).	Author-generated from SMM data	Stored in Zenodo repository (DOI: 10.5281/zenodo.19976985); file: Data.csv; RRID: not applicable
Software	Python programming language – Main language for data processing, model implementation, evaluation, and figure/table generation.	Python Software Foundation / Anaconda	Python 3.10.19; Anaconda distribution; RRID: SCR_008394
Software	TensorFlow/Keras – Deep learning framework for implementing GRU, LSTM, BiGRU, BiLSTM, CNN-hybrid, attention, and Transformer models.	TensorFlow / Keras	TensorFlow 2.20.0; RRID: SCR_016345
Software	NumPy – Numerical array processing and matrix operations.	Open-source community	NumPy 1.26.4; RRID: SCR_008633
Software	pandas – Data loading, tabular processing, and CSV/Excel output handling.	Open-source community	pandas 2.3.3; RRID: SCR_018214
Software	scikit-learn – Evaluation metrics, preprocessing, and machine-learning utilities.	Open-source community	scikit-learn 1.7.2; RRID: SCR_002577
Software	StandardScaler (z-score normalization) – Feature standardization applied using training set statistics.	scikit-learn	Included in scikit-learn 1.7.2; RRID: SCR_002577
Software	Random Forest – Machine learning baseline implementation (RandomForestRegressor).	Open-source community	scikit-learn 1.7.2; RRID: SCR_002577
Software	statsmodels – ARIMA baseline implementation.	Open-source community	statsmodels 0.14.6; RRID: SCR_016074
Software	arch – GARCH baseline implementation.	Open-source community	arch 8.0.0; RRID: not available
Software	XGBoost – XGBoost regression baseline implementation.	Open-source community	XGBoost 3.1.2; RRID: SCR_025884
Software	Transformer model – Baseline deep learning architecture for comparison.	TensorFlow / Keras	Implemented using TensorFlow 2.20.0; RRID: SCR_016345
Software	Keras callbacks (ReduceLROnPlateau) – Learning rate scheduler used during training.	TensorFlow / Keras	Included in TensorFlow 2.20.0; RRID: SCR_016345
Software	Matplotlib – Figure generation and export to PDF/SVG/PNG.	Open-source community	Matplotlib 3.10.6; RRID: SCR_008595
Software	openpyxl – Excel workbook generation and export support.	Open-source community	openpyxl 3.1.5; RRID: not available
Code	GRU.py – Complete implementation of all 13 deep-learning models, Transformer comparison, ARIMA/GARCH/XGBoost/Random Forest baselines, Diebold–Mariano tests, and figure generation.	Author-written	Available at Zenodo (DOI: 10.5281/zenodo.19976985); RRID: not applicable
Code	README_reproducibility.md – Reproduction instructions and step-by-step protocol.	Author-written	Available at Zenodo (DOI: 10.5281/zenodo.19976985); RRID: not applicable
Code	requirements.txt – Software dependencies and exact version specifications.	Author-written	Available at Zenodo (DOI: 10.5281/zenodo.19976985); RRID: not applicable
Hardware	Computing workstation – All model training, validation, testing, and figure/table generation.	ASUSTeK COMPUTER INC. (ROG Strix G634JZ_G634JZ)	Windows 11 Home 10.0.26200 Build 26200; x64-based PC; RRID: not applicable
Hardware	CPU – Central processing unit for training and inference.	Intel	Intel64 Family 6 Model 183 Stepping 1, ~2.20 GHz; RRID: not applicable
Hardware	RAM – Physical memory for all computational tasks.	ASUSTeK workstation	32,387 MB (~32 GB); RRID: not applicable
Hardware	GPU acceleration – Status of graphics processing unit utilization.	TensorFlow device query	tf.config.list_physical_devices('GPU') returns []; CUDA/cuDNN not used; RRID: not applicable
Reagent/Model	Random seed (main experiment) – Fixed seed for reproducibility of stochastic elements.	Python random / NumPy / TensorFlow	Seed = 42; RRID: not applicable
Reagent/Model	Random seeds (robustness test) – Additional seeds for multi-run stability validation.	Python random / NumPy / TensorFlow	Seeds = {1, 7, 21, 42, 2024}; RRID: not applicable