A Comparative Study of Neural Network Models for China’s Soybean Futures Price Forecasting

Abstract

Accurate prediction of soybean futures prices is crucial for agricultural risk management and market decision-making. This study systematically evaluated nine state-of-the-art deep learning models—iTransformer, TFT, TCN, TimesNet, PatchTST, TiDE, TSMixer, SOFTS, and Time-LLM—for forecasting the DCE No. 2 soybean futures price, while also examining the impact of incorporating external market variables (USFP, ER, SF). The results demonstrate that in univariate forecasting, iTransformer achieved the lowest MAPE over short (5–10 days) and long (60 days) horizons, while TCN demonstrated the most stable performance at the medium-term horizon (30 days); TimesNet attained the best RMSE, making it more suitable for handling extreme volatility and controlling tail errors. Under multivariate settings (with the introduction of USFP, ER, and SF as exogenous variables), TFT demonstrates the best overall performance, significantly outperforming the LSTM baseline model across nearly all forecast horizons. The gains from exogenous variables depend on both the forecast horizon and the choice of covariates. These findings provide empirical guidance for participants in futures markets regarding model selection and covariate configuration, supporting more precise risk management and market decision-making.

1. Introduction

Soybeans serve as both an essential food crop and a major oilseed, and their by-product, soybean meal, is a critical protein source for China’s livestock sector, particularly in swine feed [1]. In recent years, driven by economic growth and evolving dietary patterns, China’s soybean demand has continued to rise [2], with the country remaining highly dependent on international markets. According to data from the General Administration of Customs of China (GACC), China imported 105 million tons of soybeans in 2024, corresponding to an import-dependence ratio of 83.57% [3,4]. Under these conditions, China’s soybean market is highly vulnerable to external shocks such as geopolitical tensions, trade policy adjustments, extreme weather events, and exchange rate fluctuations [5]. These shocks often trigger domestic price volatility, which is then transmitted along the supply chain, affecting soybean meal availability, feed processing, livestock production, and broader food-security outcomes [6,7,8]. In the face of frequent external shocks and increasing price volatility, futures markets play a particularly important role in price discovery and risk management. Through open and competitive trading mechanisms, futures markets generate forward-looking price signals and provide effective hedging instruments that help producers, processors, traders, and investors manage market uncertainty [9,10,11,12,13]. Since the launch of soybean futures trading on the Dalian Commodity Exchange (DCE) in 1993, DCE soybean futures prices have become key benchmarks for pricing and information transmission throughout China’s soybean supply chain [14]. Accurate forecasting of soybean futures prices is therefore essential for improving risk management, procurement planning, and market monitoring.

As a variable with the dual attributes of financial time-series data and agricultural commodities, soybean futures prices exhibit seasonality, stochastic volatility, and nonlinearity [15,16,17]. Traditional time-series models rely on the assumption of stationarity in the data and struggle to handle complex nonlinear relationships [18]. Consequently, relying solely on conventional statistical models may lead to suboptimal forecasts and limit their usefulness in real-world decision-making [19]. With the rapid development of artificial intelligence, machine learning (ML) and deep learning (DL), which offer powerful high-dimensional feature extraction and nonlinear modeling capabilities, have become the main tools in financial price forecasting. In particular, deep-learning neural networks excel at handling noisy, highly chaotic time-series data, mitigate overfitting more effectively, and offer stronger generalization, making them a primary focus of current research [20,21]. For example, the Sample Convolution and Interaction Network (SCINet) has shown strong results in multi-step corn price prediction, while hybrid models such as the Convolutional Neural Network and Long Short-Term Memory mode l (CNN-LSTM) based on the Bayesian optimization (BO) algorithm (BO-CNN-LSTM), and transformer-based frameworks like Patch Time Series Transformer (PatchTST) and iTransformer, have demonstrated superior accuracy and robustness in forecasting soybean and soybean-meal futures [11,15,18,22,23]. Overall, no single neural network model is uniformly optimal across all futures contracts. Hybrid-model–based forecasting generally outperforms single-model approaches. Incorporating appropriate exogenous variables effectively enhances predictive performance [24]. The reasons for this are twofold: (1) different futures contracts, especially different agricultural futures, differ markedly in statistical properties and driving factors; and (2) neural network models vary in their emphases on memory horizon, seasonality/trend representation, integration of exogenous variables, probabilistic modeling, and computational efficiency. Therefore, it is necessary to systematically evaluate model performance for specific contracts in order to identify the most suitable architecture and provide precise tools for practical trading and risk management.

Soybean futures price forecasting has been extensively studied using neural networks. As

Table 1. Literature on soybean futures price prediction.

Futures Product	Models/Algorithms	Exogenous Variable	Reference
CN Soy Fut	PM: dynamic model averaging (DMA) and dynamic model selection (DMS) framework BM: Time-Varying Parameter (TVP); Recursive OLS-AR (3); Recursive OLS-All predictors; Random walk	Chinese soybean futures price; Chinese soybean net import; Chinese soybean spot price; U.S. soybean futures price; Trading Volume in Chinese soybean futures markets; Turnover rate in Chinese soybean futures markets; WTl Crude oil spot price; Exchange rate of USD/CNY; Baltic dry index	[27]
CN Soy Fut (#1)	PM: BO-CNN-LSTM BM: BP neural network; LSTM; CNN-LSTM	Opening price (OP); Highest price (HP); Lowest price (LP); Closing price (CP); Trading volume (TV); Transaction amount (TA); Open interest (OT)	[11]
CN Soy Fut (#1)	PM: LSTM BM: GRU; RNN	OP; HP; LP; CP; TV; TA; OT; 10-day moving average; Moving average convergence divergence; Bias ratio; Larry Williams’ percent range; Relative strength index; Rate of change; Domestic and international news; et al.	[28]
US Soy Fut	PM: Elastic Net; Support Vector Regression (SVR); Decision Tree; Random Forest; Gradient Boosting; LSTM; ANN; Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX); Seasonal Autoregressive Integrated Moving Average with exogenous variables (SARIMAX)	US dollar index; Gold (XAU/USD); Crude oil (WTI/USD); Fertilizers price index; Freight rates; Shipping rates; Weather report; Soybean planting chart; Agriculture planting chart; Bulk grain prices; Soybean future price; Import rate	[29]
CN Soy Fut	PM: LSTM BM: RNN; GRU; ANN	N/A	[30]
CN Soy Fut (#1)	PM: Attention-LSTM BM: Autoregressive Integrated Moving Average (ARIMA); SVR; LSTM	N/A	[9]
CN Soy Fut	PM: Ensemble Empirical Mode Decomposition (EEMD) and New Attention Gate Unit (NAGU) model (EEMD-NAGU) BM: SVR; LSTM; GRU; NAGU; EEMD-LSTM; EEMD-GRU; Attention-LSTM; Attention-GRU; EEMD-Attention-LSTM; EEMD-Attention-GRU;	Dow Jones Industrial Index (DJIA); S&P Dow Jones Indices Index (S&P 500); National Association of Securities Dealers Automated Quotations Index (NASDAQ)	[31]
CN Soy Fut	PM: ARIMA	N/A	[32]
CN Soy Fut	PM: LSTM BM: BP	N/A	[33]
CN Soy Fut (#1)	PM: Multistage Attention Network (MAN) BM: VAR; LSTM	CP; OP; HP; LP; Price fluctuation; Temperature index; Air pressure index; Precipitation index; Search index	[16]
CN Soy Fut Index	PM: Multi-layer LSTM BM: ARIMA; Multi-Layer Perceptron (MLP); SVR	N/A	[34]
US Soy Fut	PM: chaotic artificial neural network (CANN) BM: ANN	N/A	[35]
CN Soy Fut	PM: Two-Stage Hybrid-LSTM BM: univariate LSTM; multivariate LSTM; eXtreme Gradient Boosting	Social media text feature	[36]
CN Soy Fut (#1) US Soy Fut IT Soy ETF	PM: ICEEMDAN-LZC-BVMD-SSA-DELM (a hybrid model composed of improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN); Lempel-Ziv complexity (LZC) determination method; variational mode decomposition optimized by beluga whale optimization (BWO) algorithm (BVMD); sparrow search algorithm (SSA); deep extreme learning machine (DELM)) BM: ELM; radial basis function (RBF); deep belief network (DBN); LSTM; GRU; DELM; SSA-DELM; ICEEMDAN-DELM; ICEEMDAN-SSA-DELM; VMD-DELM; BVMD-DELM; BVMD-SSA-DELM; ICEEMDAN-LZ-BVMD-DELM	N/A	[37]

Note: CN = China; US = United States; IT = Italy; Soy = soybean; Fut = futures; #1 = contract No. 1; N/A = not applicable; PM = proposed model; BM = baseline model.

illustrates, neural network-based models underpin 12 of the 14 reviewed studies. Recurrent architectures such as RNN, LSTM, GRU, and Attention-LSTM remain the most commonly used, while several studies investigate hybrid CNN-LSTM models or complex decomposition–forecasting pipelines including EEMD-NAGU and ICEEMDAN-LZ-BVMD-SSA-DELM. Although these approaches have produced many valuable results, prior studies have also identified several inherent limitations. These include difficulties in modeling long-range dependencies, limited ability to capture multiscale temporal structures, and insufficient mechanisms for effectively incorporating nonlinear exogenous covariates [25,26]. In addition, decomposition-based hybrid models typically rely on multi-stage procedures, which not only increase computational burden but may also reduce robustness due to the propagation of decomposition errors across stages. These limitations are particularly relevant for agricultural futures, which typically exhibit long-horizon dependence, multiscale volatility characteristics, and strong exogenous influences. In recent years, newer architectures such as Time-LLM, TSMixer, SOFTS, and TiDE have demonstrated strong performance according to general time-series benchmarks, yet their potential strengths in long-horizon forecasting, efficient representation learning, and multivariate joint modeling have not been systematically evaluated in agricultural futures markets. Therefore, this study selects nine representative state-of-the-art models to conduct a consistent and comprehensive comparative assessment tailored to the forecasting characteristics of agricultural futures, thereby addressing the methodological gap in this field.

China’s soybean futures market features a dual-contract system. The No. 1 contract, grounded in domestic non-GM food soybeans, serves the food processing industry, while the No. 2 contract, tied to imported GM soybeans, is priced in direct linkage with the global market [38]. Although academic focus has historically been on the more liquid No. 1 contract, which has yielded substantial findings in price discovery [39,40,41], volatility transmission [42,43], and price forecasting [9,11,16,28], studies reveal that the No. 2 contract plays a disproportionately large role in price discovery [44], even outperforming its counterpart [45]. Given that the dominant position of U.S. soybeans in the global pricing system has been weakened in the context of U.S.–China trade frictions [41], the necessity for systematic research on the No. 2 contract, which is directly integrated with international markets, is further underscored. Therefore, as the liquidity of the No. 2 contract improves, forecasting its prices is essential not only to fill a gap in the literature but also to safeguard national food security and stabilize the operations of related industrial chains.

Soybean futures prices are co-determined by multiple factors, including global supply–demand fundamentals, macroeconomic and financial conditions, trade and logistics costs, as well as external shocks such as geopolitical conflicts and extreme weather [27,29,37,46,47]. The price formation of the No. 2 soybean contract is more directly anchored in the “import cost” mechanism. Its key determinants are concentrated in three primary aspects: (1) the CBOT soybean futures price, which represents global supply–demand dynamics and serves as the benchmark price signal; (2) the USD/CNY exchange rate, which reflects the import cost in local currency terms; and (3) ocean freight costs, which capture international transportation expenses and trade competitiveness. These three variables collectively constitute the most core and rigid components of the No. 2 contract’s pricing system—a relationship that is both economically interpretable and empirically well-supported [27,46,48,49]. Furthermore, unlike factors such as geopolitical events or extreme weather that resist consistent quantification, these variables provide transparent, high-frequency data and exhibit characteristics suggestive of exogeneity, making them more amenable to integration into deep learning models and offering a solid foundation for enhancing the robustness and interpretability of multi-step forecasts. Their exogeneity and lead–lag relationships are further empirically examined through cross-correlation analysis, as detailed in Appendix A.

Considering the above context, the purpose of this study is to systematically evaluate the predictive performance of advanced deep learning models for China’s DCE No. 2 soybean futures price and to examine the role of exogenous variables in improving model accuracy. The main innovations and contributions of this study are threefold. First, this study fills a gap in the existing literature by focusing on the DCE No. 2 soybean futures contract, which is closely linked to China’s import-dependent market structure, in contrast to the extensively studied No. 1 contract. Second, this study introduces and compares multiple state-of-the-art deep learning models, expanding the application boundaries of such methods in agricultural futures price forecasting. Third, this study incorporates key exogenous variables such as U.S. soybean futures, exchange rates, and ocean freight costs, and quantitatively evaluates their incremental value in enhancing forecasting performance.

The research process includes three main stages:

• Univariate forecasting: Under a fixed data split, we conduct a unified evaluation of Time-LLM, SOFTS, TiDE, iTransformer, PatchTST, TimesNet (Temporal 2D-Variation Modeling for General Time Series Analysis), TSMixerx, TCN, and TFT (Temporal Fusion Transformer), with the canonical recurrent neural network LSTM serving as the benchmark.
• Single-target multivariate forecasting: We take the DCE No. 2 soybean futures price as the forecasting target. Using models capable of processing exogenous variables (namely TSMixer, TCN, TFT, TiDE, and LSTM), we build multivariate models to test whether incorporating these variables improves predictive performance.
• Multi-step forecasting performance and robustness evaluation: We evaluate all models across varying forecast horizons to examine the robustness of their performance as the horizon changes. This analysis provides practical guidance for model selection across different decision cycles.

The structure of this paper is organized as follows: Section 1 introduces the research background, motivation, innovations, and objectives. Section 2 presents the methodology and data. Section 3 reports the empirical results from both univariate and multivariate forecasting experiments, followed by an evaluation of multi-step robustness across forecast horizons. Section 4 discusses the main findings, robustness verification, and practical implications, and further identifies the limitations of the study and directions for future research. Section 5 summarizes the results of the research.

2. Materials and Methods

2.1. Dataset Description

This study utilizes eight datasets across three categories: futures, exchange rates, and freight costs. Among them, the freight cost category includes five major soybean shipping routes from China’s three principal import origins (Brazil, the United States, and Argentina), which together account for approximately 96% of China’s total soybean imports [3]. These routes cover shipments from Santos (Brazil), Paranaguá (Brazil), Argentina, the U.S. Gulf Coast, and the U.S. Pacific Northwest to China. For simplicity, the freight cost variables derived from these routes are collectively referred to as SF in the subsequent analysis. The details of all variables, including abbreviations, descriptions, data sources, and descriptive statistics, are provided in

Table 2. Variable definitions and data sources.

Variable		Description	Source
Target variables	CSFP	China’s DCE No. 2 soybean futures price	Dalian Commodity Exchange Data Center
Exogenous variables	USFP	U.S. CBOT soybean futures price	China Grain and Oil Business Network Data Center
	ER	Exchange rate of USD/CNY	China Foreign Exchange Trade System
	SFS	Soybean Freight Cost (Santos, Brazil–North China)	China Grain and Oil Business Network Data Center
	SFP	Soybean Freight Cost (Paranaguá, Brazil–China)	China Grain and Oil Business Network Data Center
	SFA	Soybean Freight Cost (Argentina–Northern China)	China Grain and Oil Business Network Data Center
	SFG	Soybean Freight Cost (U.S. Gulf Coast -China)	China Grain and Oil Business Network Data Center
	SFN	Soybean Freight Cost (U.S. Pacific Northwest–China)	China Grain and Oil Business Network Data Center

Note: Data are obtained from official and verifiable sources, including the Dalian Commodity Exchange Data Center, the China Foreign Exchange Trade System, and the China Grain and Oil Business Network Data Center (institutional subscription). Public data are freely available from http://www.dce.com.cn/dalianshangpin/xqsj/lssj/index.html (accessed on 11 August 2025) and https://www.chinamoney.com.cn/chinese/bkccpr/ (accessed on 11 August 2025), while subscription-based data are available upon request from https://www.fao.com.cn/DataCenter.html (accessed on 7 August 2025).

and

Table 3. Descriptive statistics of the dataset.

Variable	Mean	Max	Min	Standard Deviation	Coefficient of Variation	Unit
CSFP	3957.00	5751.00	2709.00	655.29	0.17	CNY/T
USFP	2795.26	4289.14	1906.37	541.60	0.19	CNY/T
ER	6.70	7.81	6.09	0.39	0.06	-
SFS	45.67	143.00	13.70	22.78	0.50	USD/T
SFP	44.39	140.06	12.20	22.40	0.50	USD/T
SFA	48.88	140.00	21.10	21.14	0.43	USD/T
SFG	51.86	139.00	20.00	20.04	0.39	USD/T
SFN	29.41	100.00	11.00	13.37	0.45	USD/T

Note: USFP data were originally denominated in U.S. dollars and converted into Chinese yuan (CNY) using the contemporaneous USD/CNY exchange rate obtained from the China Foreign Exchange Trade System.

, while their temporal dynamics are illustrated in Appendix B.1.

2.2. Data Preprocessing

This study constructs the raw futures price series using the contract with the largest open interest. To account for the non-overlapping public holidays between China and the U.S. and to maintain a continuous sequence of trading observations, non-trading days (weekends and holidays) were excluded based on the trading calendar of Chinese soybean futures. This ensures regular time steps required for deep learning model training and evaluation. Price movements on the first trading day following a non-trading period (e.g., Monday) inherently incorporate information and expectations accumulated during the preceding non-trading days; thus, potential jumps caused by macroeconomic announcements or policy events are reflected in subsequent observations rather than omitted. For missing values in exchange rates and shipping freight, they were supplemented using forward filling and linear regression fitting, respectively.

The sample period spans from 1 January 2007 to 31 December 2024, comprising 4365 valid records. The dataset was split chronologically, with the first 90% allocated to the training set and the remaining 10% reserved for validation and testing. All continuous features were normalized using the Robust Scaler, which rescales data based on the median and interquartile range (IQR) to mitigate the influence of outliers.

Specifically, the transformation is defined as

$$X^{\prime }={\displaystyle \frac{X-\mathrm{Median}\left(X\right)}{\mathrm{IQR}\left(X\right)}}$$

(1)

This approach enhances robustness against weak outliers and improves model convergence stability.

Before introducing the model architectures, the complete end-to-end workflow of the forecasting pipeline is illustrated in Figure 1. This diagram summarizes the procedures of data splitting, preprocessing, TPE-based hyperparameter optimization, model training, and performance evaluation.

2.3. Research Methods

This study selects nine representative models from five mainstream neural network architectures: MLP, CNN, Transformer, LLM, and RNN. The selected models include SOFTS, TiDE, TSMixerx, TCN, TimesNet, PatchTST, iTransformer, TFT, and Time-LLM. LSTM serves as a classical RNN benchmark model, providing the baseline for comparative evaluation. Each architecture embodies distinct modeling principles and strengths in capturing temporal dependencies and feature interactions, thereby offering a fair and diverse foundation for systematic comparison across representative neural forecasting paradigms.

2.3.1. MLP-Based Models

• SOFTS

SOFTS is an efficient MLP-based model that streamlines the forecasting process and enhances prediction accuracy. SOFTS incorporates the STar Aggregate–Redistribute (STAR) module, which implements a centralized strategy that first aggregates information across channels to construct a global core representation and then redistributes it to individual channels for fusion, thereby enabling efficient cross-channel interaction [50]. By replacing distributed pairwise interactions with this centralized mechanism, STAR reduces the typical quadratic complexity to linear, substantially improving scalability and computational efficiency.

• TiDE

TiDE is an encoder–decoder model architecture based on MLP, which comprises four core components: feature projection, dense encoder, dense decoder, and temporal decoder [18]. The dynamic covariates per time-point are mapped to a lower dimensional space using a feature projection step. Then the encoder combines the look-back along with the projected covariates with the static attributes to form an encoding. The decoder maps this encoding to a vector per time-step in the horizon. Then a temporal decoder combines this vector (per time-step) with the projected features of that time-step in the horizon to form the final predictions. We also add a global linear residual connection from the look-back to the horizon. The model retains both the simplicity and speed of linear models while effectively capturing nonlinear dependencies and incorporating covariate information [51].

• TSMixer

TSMixer is based on mixing operations along both the time and feature dimensions to extract information efficiently. The time-domain MLPs are shared across all of the features, while the feature-domain MLPs are shared across all of the time steps. The interleaving design between these two operations efficiently utilizes both temporal dependencies and cross-variate information while limiting computational complexity and model size [52].

2.3.2. CNN-Based Models

• TCN

TCN is a CNN-based architecture tailored for sequence data, particularly time series. It enforces causality via causal convolutions so that the output at time t depends only on inputs at t and earlier, thereby preventing any leakage of future information. Dilated convolutions expand the receptive field exponentially, enabling the model to capture long-range dependencies. While residual connections alleviate vanishing gradients, support deeper networks, and improve training stability [53].

• TimesNet

Based on the multi-periodicity of time series, Wu et al. [25] proposed the TimesNet with a modular architecture to capture the temporal patterns derived from different periods. For each period, to capture the corresponding intraperiod and interperiod variations, a TimesBlock is designed within the TimesNet, which can transform the 1D time series into 2D space and simultaneously model the two types of variations by a parameter-efficient inception block. Thus, TimesNet can achieve a more effective representation learning than directly from 1D time series [25].

2.3.3. Transformer-Based Models

• PatchTST

The Transformer has become a widely used architecture in modern deep learning. Nie [54] introduced PatchTST, an effective Transformer-based model design for time series forecasting tasks, by incorporating two key components: patching and a channel-independent structure. The Patch module segments the series into temporal patches using a chosen window size and stride. These patches are then fed to the Transformer, whose self-attention captures global dependencies among patches and thereby improves predictive performance [18]. This design enables the model to capture local semantic information and benefft from longer look-back windows [54].

• iTransformer

iTransformer modifies none of the native components of the Transformer architecture. Instead, it simply applies the attention and feed-forward network to inverted dimensions. iTransformer regards independent series as variate tokens to capture multivariate correlations by attention and utilize layer normalization and feed-forward networks to learn series representations [55]. iTransformer enhances the Transformer family with promoted performance, stronger generalization across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting.

• TFT

TFT is an attention-based deep neural network (DNN) architecture [26,56]. As it retains the encoder–decoder backbone of the Transformer, this study categorizes it under the Transformer architecture. Lim [26] proposed the TFT architecture with the following key components: it accepts static metadata, time-varying past inputs, and time-varying a priori known future inputs as its input sources. Variable Selection is used for the judicious selection of the most salient features based on the input. Gated Residual Network blocks enable efficient information flow with skip connections and gating layers. Time-dependent processing is based on LSTMs for local processing, and multi-head attention for integrating information from any time step.

2.3.4. LLM-Based Models

Time-LLM is a reprogramming framework that adapts large language models (LLMs) for time-series forecasting while keeping the backbone unchanged [57]. The framework comprises three components: (1) patch tokenization of the input time series followed by a customized embedding layer; (2) cross-modal reprogramming of the patch embeddings using condensed textual prototypes, complemented by task-specific prompt prefixes that guide the transformation of the patches; and (3) a projection head that maps the LLM outputs back to the time-series domain to produce forecasts. Through this reprogramming approach, LLMs can act as effective few-shot and even zero-shot time series learners, outperforming specialized forecasting models.

2.4. Experimental Evaluation Metrics

Three main evaluation metrics were used to evaluate the model’s accuracy in this study, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) calculated as

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|$$

(2)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(3)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right|\times 100\mathrm{\%}$$

(4)

where $y_i$ and ${\widehat{y}}_i$ denote the observed and forecasted prices of Chinese soybean futures, respectively, and $n$ is the number of observations in the out-of-sample period. Lower MAE, RMSE, and MAPE values indicate better model accuracy, with MAE being less affected by outliers, RMSE being particularly sensitive to large errors, and MAPE providing a relative error measure, making it suitable for comparison across different datasets [22].

To ensure consistency in model evaluation, this study specifies the ranking of performance criteria as follows: the primary criterion is the lowest MAPE, which measures forecast accuracy and allows comparison across different horizons; the secondary criterion is the RMSE, which reflects the variability of prediction errors; when models exhibit similar average MAPE values, the model with more stable performance is preferred.

2.5. Hyperparameter Optimization

Hyperparameter optimization was conducted using the Tree-structured Parzen Estimator (TPE) algorithm implemented in the HyperOpt library. The TPE method constructs a probabilistic surrogate model of the objective function based on historical evaluation results, allowing for adaptive exploration of the hyperparameter space and improving both search efficiency and model stability. Unlike traditional grid search or random search methods, TPE does not directly model the objective function $f\left(x\right)$. Instead, it estimates two probability density functions:

$$g\left(x\right)=p\left(x∣y<y^{*}\right)$$

(5)

and

$$l\left(x\right)=p\left(x∣y\ge y^{*}\right)$$

(6)

where $y^{*}$ denotes a performance threshold (e.g., the top quantile of evaluation scores).

The algorithm then selects the next candidate hyperparameter configuration by maximizing the Expected Improvement (EI) criterion:

$$\mathrm{E}\mathrm{I}\left(x\right)={\displaystyle \frac{g\left(x\right)}{l\left(x\right)}}$$

(7)

which measures the likelihood that a new configuration $x$ will outperform the current best result.

During optimization, all models share a unified hyperparameter search space, with the MAE used as the optimization objective due to its robustness to outliers and stable gradient behavior. The detailed search ranges are summarized in

Table A1. Model Configurations and Hyperparameter Search Space.

Category	Parameter	Setting/Search Space
General	learning_rate	10−5–10−2 (log-uniform)
	batch_size	{8, 16, 32}
	input_size	{365, 730}
	max_steps	1000
	random_seed	1–10
iTransformer	d_model	64
	n_heads	4
TiDE	hidden_size	256
	decoder_output_dim	{8, 16, 32}
	num_encoder_layers/num_decoder_layers	{1, 2, 3}
PatchTST	patch_len	{16, 24}
	n_heads	{4, 16}
TCN	n_layers	4
	kernel_size	3
	dilation	Fixed as {1, 2, 4, 8}
TFT	hidden_size	64
	n_heads	4
SOFTS/TimesNet/TSMixer	model_dim	{64, 128}
LSTM	hidden_size n_layers	200 {1, 2, 3}

in Appendix B.2.

This probabilistic optimization strategy enables efficient exploration of high-dimensional hyperparameter spaces while maintaining low computational overhead, making it well-suited for deep learning forecasting models with complex parameter interactions.

2.6. Computational Setup

All experiments were conducted on a workstation equipped with two NVIDIA A100 GPUs (40 GB memory each), two Intel(R) Xeon(R) Gold 6132 CPUs (2.60 GHz), and 512 GB RAM. The software environment consisted of Python 3.10, PyTorch 2.5.1, Ray Tune 2.20, and CUDA 12.4. This configuration ensured adequate computational resources for efficient model training, hyperparameter optimization, and experimental reproducibility.

3. Results

3.1. Results: Univariate Forecasting

This study conducts time-series modeling based on the price data of China’s No. 2 soybeans futures contract. A systematic comparative analysis of nine advanced deep learning models reveals distinct differences in their aggregate performance throughout the forecasting horizon. As shown in

Table 4. Performance evaluation of the models (multi-horizon average over 1–90 steps).

Framework	Models/Algorithms	MAE	MAPE	RMSE
MLP	SOFTS	140.9926	0.0407	187.8455
	TiDE	388.5366	0.1118	459.8178
	TSMixerx	343.5763	0.0993	419.1471
CNN	TCN	216.5880	0.0631	291.8825
	TimesNet	147.3828	0.0412	184.7208
Transformer	PatchTST	206.5781	0.0600	270.9045
	iTransformer	133.4171	0.0387	186.6440
	TFT	395.0730	0.1157	558.9772
LMM	Time-LLM	438.0608	0.1260	505.6690
RNN	LSTM	237.9026	0.0653	264.0886

, iTransformer, TimesNet, and SOFTS achieve the best overall performance on this dataset, significantly outperforming the LSTM baseline (MAE = 237.90, MAPE = 0.0653, RMSE = 264.09) across all three metrics. Specifically, iTransformer achieves the best MAE and MAPE, with reductions of 43.9% and 40.7%, respectively; its RMSE also secures a top result, exhibiting a 29.3% decrease relative to the LSTM baseline. Notably, TimesNet attains the best RMSE and demonstrates greater stability in capturing price spikes and large swings. SOFTS is close to optimal across all three metrics (MAE = 140.99, MAPE = 4.07%, RMSE = 187.85) and, as a lightweight MLP-based approach, is well suited to latency-sensitive inference scenarios.

In contrast, TFT records a significantly higher RMSE of 558.98, which is approximately three times that of iTransformer, TimesNet, and SOFTS. It exhibits weaker error control and limited robustness on samples with extreme volatility. Time-LLM performs substantially worse on all three metrics (MAE = 438.06, MAPE = 12.60%, RMSE = 505.67). This indicates that a minimal adaptation strategy for general-purpose LLMs [57], without dedicated time-series retraining, may be insufficient to achieve the performance level of models specifically designed for forecasting [58].

3.2. Results: Univariate Target with Exogenous Covariates

To ensure a fair and reproducible comparison, the multivariate analysis was limited to those model implementations with inherent support for exogenous variables (namely, TSMixerx, TCN, TFT, TiDE, and LSTM). As shown in Figure 2, TFT demonstrates the best overall performance after the incorporation of the exogenous variables USFP, ER, and SF. Specifically, with all three variables included, TFT’s MAE, MAPE, and RMSE are reduced by 41.0%, 37.6%, and 26.2%, respectively, compared to the multivariate LSTM benchmark. TiDE ranks second, showing only a marginal improvement over LSTM.

A detailed comparison of each model’s performance before and after the inclusion of exogenous variables is presented in

Table 5. Impact of exogenous variables on forecasting performance metrics (MAE, MAPE, RMSE).

External Variables	Model	ΔMAE (%)	ΔMAPE (%)	ΔRMSE (%)
USFP	TFT	+55.4	+55.9	+59.0
	TiDE	+44.8	+44.4	+35.9
	TSMixer	−2.1	−1.0	+5.6
	TCN	−123.2	−122.5	−127.0
	LSTM	−8.9	−13.5	−13.6
ER	TFT	+56.5	+57.2	+60.5
	TSMixer	+19.2	+19.7	+24.7
	TiDE	−20.3	−20.0	−18.7
	TCN	−79.7	−76.9	−49.9
	LSTM	−15.9	−18.5	−15.3
SF	TFT	+57.6	+57.9	+59.9
	TSMixer	−1.6	−1.8	−4.0
	TiDE	−1.9	−2.0	−3.1
	TCN	−153.4	−146.4	−128.3
	LSTM	−100.9	−104.1	−107.0
USFP + ER + SF	TFT	+59.6	+59.9	+61.3
	TiDE	+37.0	+37.5	+36.8
	TSMixer	+19.6	+19.8	+16.8
	TCN	−160.2	−152.6	−103.0
	LSTM	−13.9	−13.7	−11.2

Note: All “Δ” values in the table represent the magnitude of change relative to the univariate version of each respective model; “+” indicates a decrease in the metric (denoting better performance), while “−” indicates an increase in the metric (denoting worse performance).

. The results reveal that (1) TFT exhibits significant performance improvements under any single-variable setting as well as the full three-variable combination; (2) TiDE demonstrates clear gains from USFP and the three-variable combination, but its performance exhibits instability when ER or SF are added individually; (3) TSMixer derives the most benefit from ER, with only marginal gains from USFP and SF; and (4) both TNC and LSTM exhibit performance degradation after the introduction of any exogenous variables, with SF causing the most pronounced deterioration. This issue primarily stems from architectural limitations: TCN and LSTM lack explicit mechanisms for variable selection, gating, or attention, which hinders their ability to automatically learn and align the complex lagged relationships between exogenous variables and the target series. When exposed to noisy or temporally misaligned external features (e.g., SF), these models fail to filter out irrelevant signals effectively, leading to noise amplification during the prediction process and a consequent degradation in performance.

Analyzing the marginal contributions of the exogenous variables reveals distinct patterns (Table 5). USFP exhibits strong comovement with the target series; however, translating this signal into predictive gains requires models with variable-selection and lag-alignment capabilities. In this regard, TFT and TiDE show the clearest improvements: TFT demonstrates a reduction exceeding 50% across all three error metrics, while TiDE achieves reductions of 35–45%. ER is an information-dense variable whose cadence aligns closely with price fluctuations. TFT demonstrates a remarkable ability to leverage the ER signal, achieving the largest reduction in RMSE (60.5%) among all models. Similarly, TSMixer also benefits from the incorporation of the ER variable, with decreases of 19% to 25% across all metrics. By contrast, SF shows the highest noise level among all exogenous variables, as indicated by its large Coefficient of Variation in Table 3. It also exhibits noticeable lag mismatches, as illustrated in Appendix A.2. Given these characteristics, models that lack sufficient representational capacity or explicit variable-selection mechanisms are more likely to experience performance degradation when SF is included. Only TFT registers a significant gain, whereas the performance of TSMixer, TiDE, TCN, and LSTM deteriorates, with that of TCN degrading the most.

In summary, while exogenous variables can be beneficial for forecasting, their efficacy is highly contingent on model architecture. Specifically, only models equipped with robust variable-selection mechanisms and lag-alignment capabilities are capable of reliably translating these external signals into reproducible performance gains.

3.3. Results: Multi-Horizon Performance Comparison

For the model whose hyperparameters were optimized on the validation set, a single-origin multi-step forecast was performed on the test window. We reported the cumulative temporal mean of MAE, MAPE, and RMSE over increasing forecast horizons (1-k steps, where k ∈ {5, 10, 30, 60}). Since MAE, MAPE, and RMSE exhibit nearly identical trends across varying forecast horizons, we hereafter present the detailed analysis using MAPE as a representative metric.

Without exogenous variables, iTransformer attains the lowest MAPE in the short term (recording 0.0073 and 0.0112 for 5-day and 10-day horizons, respectively), followed closely by TFT, TCN and PatchTST. It also demonstrates a clear advantage over the baseline LSTM (0.0741 and 0.0698 for the same short-term horizons). At the mid-horizon (30 days), TCN becomes slightly best (0.0172), with PatchTST (0.0183) and iTransformer (0.0188) very close. At the long horizon (60 days), iTransformer regains the lead (0.0387), followed by SOFTS and TimesNet, while TFT/TiDE/TSMixerx degrade more visibly with horizon length. Consistent with expectations, prediction errors generally increase with the forecast horizon. However, iTransformer demonstrates robust performance across all horizons, while TCN exhibits greater stability at medium-term horizons (see Figure 3).

When all exogenous variables (USFP, ER, and SF) are incorporated simultaneously, TFT achieves the lowest MAPE across all forecast horizons (5, 10, 30, and 60 days: 0.0061, 0.0106, 0.0150, and 0.0464, respectively), significantly outperforming benchmark LSTM model as well as other deep learning architectures such as TCN, TSMixerx, and TiDE. With single exogenous variables, TFT remains best across all horizons for ER and SF. When augmented solely with USFP, TFT exhibits a slightly higher MAPE (0.0510) compared to the LSTM baseline (0.0440) specifically at the 60-day horizon, while maintaining strong predictive performance at shorter horizons. These results indicate that the gains from exogenous variables depend on both the forecast horizon and the type of covariate (see Figure 4).

To further characterize the interaction between exogenous inputs and forecast horizons, we focus on TFT, whose architecture natively supports covariates and exhibits strong multivariate performance, and quantify its gains under the same evaluation protocol as the univariate (CSFP) baseline. Relative to its univariate baseline, TFT exhibits a systematic reduction in MAPE as the forecast horizon extends in the ALL (USFP + ER + SF) exogenous variables scenario, achieving reductions of 35.5%, 38.2%, 22.2%, and 59.9% at 5, 10, 30, and 60 days, respectively. With single sources, USFP may provide negligible or even slightly negative benefits at very short horizons, whereas ER, SF, and the full variable set (ALL) consistently lead to lower MAPE and more stable performance across horizons (see Figure 5).

4. Discussion

4.1. Model Performance Discussion

The study found that in the univariate prediction setting, iTransformer performs better on MAE and MAPE, whereas TimesNet achieves the best RMSE. iTransformer embeds the entire univariate history as a single “token” and employs a shared feed-forward network (FFN) for strong sequence encoding, effectively capturing intrinsic attributes such as amplitude, periodicity, and trend. This architectural choice underpins its performance advantage on univariate tasks [55]. Souto’s et al. [59] analysis of stock realized-volatility forecasting corroborates TimesNet’s strength in mitigating the impact of extreme market movements, resulting in a substantially lower RMSE. Therefore, TimesNet is more suitable for long-horizon forecasting and for scenarios that demand higher consistency and robustnesss [25,59]. The statistical significance of these performance differences has been confirmed by Wilcoxon signed-rank tests (Appendix C.1). After incorporating exogenous variables, TFT achieved superior overall performance, which is attributable to its built-in variable selection networks and interpretable attention mechanisms [26]. Likewise, Sakib et al. [60] demonstrates that TFT achieves superior accuracy and robustness in solar irradiance forecasting when integrated with multiple meteorological exogenous variables.

This study employs a rigorous out-of-sample evaluation protocol: after temporal data segmentation, a standardizer is fitted exclusively on the training set to prevent data leakage; automated hyperparameter optimization is performed on the validation set; and a one-time “blind test” is ultimately conducted on the test set. All performance metrics are calculated on the inverse-normalized original price scale to ensure the evaluation results directly reflect actual price prediction errors. This single-origin forecasting framework guarantees that test set data remains entirely unused during the training process, significantly enhancing the reliability of the evaluation outcomes. By utilizing cumulative average errors (e.g., MAE, MAPE, RMSE) over the prediction horizon rather than single-step errors for model performance measurement, this study places greater emphasis on the model’s overall stability throughout the entire forecast interval rather than on short-term precision. This methodological approach differs from the evaluation frameworks (e.g., single-step prediction or dynamic rolling prediction) employed in some studies [9,11,37] for soybean futures price prediction models, leading to a “conservative” appearance in direct performance comparisons. Additionally, factors such as the quotation unit, sample period range, dataset scale, forecast horizon setting, selection of futures contract types, and market conditions during the sample period can all influence the model’s final predictive performance. This study is among the first to systematically integrate and apply a range of new-generation deep learning models for forecasting the price of soybean No. 2 futures contract in China, incorporating external market information (e.g., USFP, ER, SF) to construct a comparative analysis framework. The research conclusions demonstrate robustness across multiple relative error metrics, providing an empirical foundation and decision-making reference for subsequent model selection and covariate configuration strategies.

Furthermore, the continuity of futures price series can be compromised by artificial jumps at contract rollovers when splicing data based on maximum open interest. To ensure that our model comparisons are not biased by these potential artifacts, we conducted a focused robustness check by forecasting 5-day log-returns. The results demonstrated a high consistency in model rankings between the return series and the original price series (see Appendix C.2). Top-performing models (e.g., iTransformer, TFT, TCN, PatchTST, TimesNet, SOFTS) remained at the forefront, while weaker models (e.g., TSMixerx, LSTM, TimeLLM) consistently lagged. This stability, confirmed even under the sensitive test of short-term return forecasting, strongly indicates that the relative performance of the models reflects their genuine capacity to capture underlying market dynamics, rather than an overfitting to rollover-induced noise.

4.2. Exogenous Covariates Discussion

While this study incorporates several exogenous variables (e.g., USFP, ER, SF) based on economic relevance and prior literature, it is also important to recognize that not all exogenous information improves model performance. Noman et al. [61] finds that irrelevant exogenous variables harm performance in energy-sector wind-speed forecasting. López-Andreu et al. [62] found that adding multiple sets of exogenous variables to several neural models (e.g., Time2Vec-Transformer, BiLSTM, MDN-BiLSTM) often led to significant performance deterioration or minimal gains. Only a few architectures remained relatively stable when the added variables were highly correlated with the target. This suggests that irrelevant or noisy features can impair a network’s generalization capability. In this study, we observe that USFP and ER typically deliver significant gains (e.g., for TFT, TiDE, and TSMixer), consistent with the literature on the co-movement between U.S. and Chinese soybean prices and on exchange-rate effects on agricultural prices and imports [46,48,63]. Conversely, SF often exhibits significant time lags and is highly susceptible to policy changes and supply–demand dynamics. Models lacking inherent variable selection mechanisms and robust temporal alignment capabilities are particularly susceptible to performance degradation when such features are incorporated. Related research also reports asymmetric and time-varying causality and lead–lag relations between freight rates and commodity prices, indicating that the direction and timing of influence can differ across markets and periods [64].

Overall, this study focuses on predictive accuracy rather than structural causality. The relationships captured by the deep learning models represent data-driven statistical dependencies and dynamic associations among market variables, rather than explicitly modeled causal mechanisms. In addition, the inclusion of the exchange rate variable reflects unhedged market conditions, where currency fluctuations are directly embedded in observed prices. Consequently, the proposed predictive framework is most applicable to market scenarios in which exchange rate risks are not explicitly neutralized through hedging strategies.

4.3. Model Applications Discussion

This study covers nine models with distinct architectures and capabilities. Based on the experimental results and computational costs, we propose the following recommendations: (1) For high-frequency, low-latency univariate forecasting, we recommend iTransformer or SOFTS; to manage extreme volatility and control tail risk, TimesNet is more suitable. (2) For multivariate long-sequence forecasting that requires a balance of low computational cost and solid accuracy, pure-MLP architectures such as TiDE, and TSMixerx are highly effective options; when highly informative exogenous covariates (e.g., USFP, ER) are available and medium- to long-horizon forecasts are needed, TFT is a superior choice with its strong overall performance and built-in uncertainty quantification capabilities. (3) TCN can serve as a computationally efficient baseline model for rapid validation. Furthermore, under the present evaluation framework, Time-LLM and PatchTST failed to outperform baseline or alternative models significantly. Thus, they are not currently recommended as primary choices, though their potential in other contexts remains unexplored.

In addition, the proposed forecasting framework provides quantitatively grounded insights for market operations and policy formulation. Specifically, the best-performing model (TFT) that integrates exogenous variables (USFP, ER, and SF) achieves a 5-day MAPE of 0.6% and maintains a 10-day MAPE of 1.06%. Given the average training-set price of CNY 3945 per ton, these levels of accuracy correspond to average absolute deviations ranging from approximately CNY 24 to 42 per ton, indicating that the model can capture short-term price dynamics with high stability. Such predictive precision offers a solid basis for forward-looking applications in risk monitoring and inventory planning in China’s soybean market. The identified lead–lag relationships between domestic and external factors offer valuable guidance for optimizing hedging strategies, for instance by leveraging the one-week leading effect of SF or the synchronous movement of USFP to dynamically adjust hedge ratios and timing. Moreover, the sensitivity of CSFP to external cost factors reveals the transmission channels of global price shocks to domestic markets, providing policy insights into margin regulation, import timing, and supply-chain stabilization. Overall, the results highlight the framework’s potential to support data-driven decision-making and enhance the robustness of risk management in China’s soybean futures market.

4.4. Limitations and Future Work

Inevitably, this study has several limitations. Although the robustness check using log-return forecasting in this study confirmed that contract rollover gaps did not affect the core conclusions of our model comparison, it should be noted that the continuous series constructed by directly splicing dominant contracts based on open interest has inherent methodological limitations in terms of continuity. Future research could further adopt professional methods such as back-adjusted or ratio-adjusted techniques to construct continuous contracts, thereby more precisely isolating and quantifying the impact of the rollover effect itself on forecasting performance. Secondly, differences in implementation maturity among deep-learning frameworks resulted in only models with stable multivariate and exogenous-covariate support (TFT, TCN, TiDE, TSMixerx and LSTM) being included in the multivariate experiments. Although other advanced architectures such as SOFTS, TimesNet, iTransformer, PatchTST, and Time-LLM are theoretically capable of handling multivariate inputs, their publicly available implementations are primarily tailored for benchmark tasks and currently lack a unified and stable interface for the single-target with exogenous covariates design adopted in this study. This methodological boundary may limit the comprehensiveness of cross-model benchmarking but ensures experimental consistency and reproducibility. Furthermore, this study has not explicitly incorporated such event-type information (e.g., trade friction, pandemics, policy adjustments) into the exogenous variables. The limited coverage of external covariates may lead to distributional shifts during state transition phases, consequently compromising model generalization and robustness.

To address the above limitations, future research should be focused on two main directions. On the data-processing side, future studies adopt back-adjusted and ratio-adjusted continuous series with rolling weights, and include features such as days to expiry, near–far month spreads, and roll yield, accompanied by sensitivity analyses. On the modeling side, future research could extend single-target, multi-covariate comparisons to include iTransformer and related models, and add proxy variables for tariff changes, pandemics and policy uncertainty. In addition, hybrid feature-learning architectures and attention-based fusion mechanisms may be explored to enhance the integration of multiple exogenous variables, improve interpretability through dynamic feature weighting, and strengthen forecasting robustness. Furthermore, the paper’s main results are based on a single-origin evaluation and are reported as cumulative averages over intervals, which stably reflect the overall level across different forecast horizons; these analyses could be supplemented later with a rolling-origin approach to align with mainstream benchmarks.

5. Conclusions

This study is among the first to systematically apply a range of deep learning neural network models to forecast the DCE No. 2 soybean futures price, evaluating their performance while integrating external market information. The findings indicate that in univariate forecasting, iTransformer achieved the lowest MAPE over short (5–10 days) and long (60 days) horizons, while TCN demonstrated the most stable performance at the medium-term horizon (30 days); TimesNet attained the best RMSE, making it more suitable for handling extreme volatility and controlling tail errors. Under multivariate settings (with the introduction of USFP, ER, and SF as exogenous variables), TFT demonstrates the best overall performance, significantly outperforming the LSTM baseline model across nearly all forecast horizons. However, the gains from exogenous variables depend on both the forecast horizon and the choice of covariates. This study provides practitioners with actionable guidance for model selection and covariate configuration and points the way toward future improvements in broader covariate coverage, futures contract data processing, and model evaluation methods.