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 ac....

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 s....

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