## 1 Introduction  
In the dynamic arena of financial markets, futures arbitrage continues to be a pivotal subject for scrutiny among investors and scholars. This strategy is integral to capitalizing on profit avenues discerned through meticulous analysis and the tactical exchange of futures contracts, by capitalizing on the variances in pricing that occur in diverse markets over time [1]. To achieve successful arbitrage, it typically demands advanced forecasts of market trajectories and asset pricing volatilities. Price, which is a paramount factor in the ebbs and flows of trading activities, carries significant implications for the expansion of the market and the welfare of its participants. As a result, predicting price trends is an essential component of research in financial investment and a foundational element in devising strong arbitrage tactics. Transitioning from the fundamental theory of futures arbitrage, early attempts to predict commodity futures prices were grounded in standard econometric methods. Historically, these methods were defined by the groundbreaking work of academics, such as the ARCH model introduced by [PERSON] in 1982, which explained time-varying volatility for economic time series data [2]. Following this innovation, a multitude of statistical models emerged, refining the approach to predict financial market behaviors. Notably, in 1986, [PERSON] presented the GARCH model, enhancing the ARCH concept and tailoring it more explicitly to financial datasets [3]. These econometric models, with the GARCH model in particular, were not only used in alignment with traditional regression techniques, but they also uniquely accounted for fluctuating error variance, facilitating a more nuanced understanding of market volatility--a key component in investor decision-making. A significant milestone was achieved with [PERSON]'s study in 2001, which successfully applied GARCH-based methods for short-term crude oil price forecasts [4]. Despite their empirical successes, challenges have persisted with these traditional models, primarily due to the intricacy and dynamic nature of financial data, which present nonlinear characteristics and time-sensitive elements that traditional mathematical models struggle to encapsulate fully. The advent of machine learning techniques in the financial sector has ushered in a new era for algorithmic trading. Currently, researchers in related fields are primarily concentrating on two aspects: the extraction of Alpha factors and the optimization of synthetic models. Factor mining, which is based on artificial intelligence algorithms, has evolved beyond the traditional approach of establishing clear investment logic relationships to mine and screen factors. Instead, it has become more adaptable, extracting and learning valuable information from relational events and sentiment data to enhance the efficiency of investment decisions. For instance, deep learning models can analyze unstructured data such as news articles and social media posts by natural language processing (NLP) technology. It allows models to capture market sentiment and potential influencing factors and enhance the precision of spread predictions. Recent literature corroborates that deep learning models excel at distilling crucial features from complex data and adeptly applying these insights to new contexts [5]. An accumulation of research underscores the efficacy of machine learning techniques in anticipating futures prices. Early initiatives, such as [PERSON]'s 1993 study [6], employed neural network (NN) algorithms for predicting gold futures prices, showing a marked improvement over traditional time series approaches. The competitive edge of NNs was further highlighted by [PERSON] and [PERSON]'s 2006 comparison [7], which found NNs to outperform ARMA and GARCH models in crude oil price forecasting. Extending this success, [PERSON] et al., (2017) [8] applied neural networks to project S&P and gold futures prices, yielding promising outcomes.