## 4 Experiments
### Data  
We gathered historical price data for rebar and HRC futures from the Shanghai Futures Exchange, covering the period from December 2020 to 15 March 2023. This dataset included 5 min K-line data comprising the open, close, high, and low prices for each contract. To construct a meaningful spread series, we calculated the price difference between the two futures types at each time point, forming a new time series used as the model input. A preliminary correlation analysis showed that the rebar and HRC futures exhibited a high correlation coefficient of 0.984, supporting their use as a meaningful spread pair for financial forecasting tasks. To improve model robustness and generalizability, we also incorporated a second dataset consisting of CSI 300 Index 1 min K-line closing prices, spanning from January 2019 to December 2024. This high-frequency dataset provides finer temporal resolution and extends beyond the primary dataset's training period, enabling evaluation under diverse market conditions and enhancing the model's real-world applicability. Both datasets were used independently for model training and testing across different experiments. The inclusion of diverse time frequencies and underlying instruments allows the proposed model to be assessed under varying levels of volatility, structural complexity, and noise--factors that are common in real-world financial time series. Data Description and Preprocessing  
The experiments in this study utilize two datasets to ensure the robustness and generalizability of the proposed model. The first dataset comprises historical 5 min K-line data for rebar and hot-rolled coil (HRC) futures, collected from the Shanghai Futures Exchange. It spans from December 2020 to 15 March 2023, and includes the open, close, high, and low prices for each time interval. This period includes significant market events and structural changes post-COVID-19, such as supply chain disruptions, commodity price volatility, and macroeconomic policy shifts, making it particularly relevant for evaluating forecasting model robustness under non-stationary financial environments. In addition, the availability of high-frequency futures data beyond this point was constrained by data access limitations from the Shanghai Futures Exchange. To enhance model generalization, we also incorporated a second high-frequency dataset (CSI 300, January 2019-December 2024) which extends the evaluation range beyond the main training period. To prevent data leakage and ensure fair evaluation, both datasets were chronologically split into training and testing sets. Specifically, 80% of each dataset was used for training, and the remaining 20% was reserved for testing. To ensure reproducibility, the rebar and HRC 5 min K-line dataset contains 184,529 data points, with 147,623 used for training and 36,906 for testing. The CSI 300 1 min dataset includes 292,080 data points, from which 233,664 were used for training and 58,416 for testing. All splits were conducted in strict chronological order to avoid data leakage and preserve the temporal structure of financial time series. During IGWO-based hyperparameter tuning, 10% of the training data was further allocated as a validation set to guide model selection. No k-fold cross-validation was employed, as maintaining temporal order is essential for time series forecasting. This ensures that the model is evaluated exclusive. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & **Python** & \multirow{2}{*}{**Memory**} & \multirow{2}{*}{**GPU**} & \multirow{2}{*}{**System**} & \multirow{2}{*}{**CUDA**} \\  & **Version** & & & & \\ \hline Parameter & Python 3.9 & 16G & GTX 4060 ti & Windows & CUDA12.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental environment. As part of the preprocessing, the input features were normalized to facilitate model convergence. Table 2 summarizes the basic statistical properties of the spread data (used as model input), including the mean, standard deviation, and value range (minimum and maximum).