## 1 Introduction  
The rapid development and intensifying competition in the FMCG sector have underscored the critical importance of medium- and long-term sales forecasting in optimizing supply chains, managing inventories, and informing strategic market decisions [1]. In recent years, the FMCG industry has witnessed significant changes driven by evolving consumer preferences, the rise of e-commerce, and increasing supply-chain management demands. These factors have not only altered the competitive landscape but also heightened the complexity of supply-chain management, making accurate forecasting more essential than ever for businesses to stay competitive and responsive to market dynamics. However, the volatile and complex nature of FMCG markets presents significant challenges for existing forecasting methodologies. Conventional models often struggle to effectively address multidimensional dynamic factors, such as price fluctuations, promotional campaigns, and macroeconomic conditions, particularly when it comes to capturing complex temporal dependencies and long-term trends. For example, the author [PERSON] used the k-Nearest Neighbors (k-NN) algorithm for sales prediction in the FMCG sector [2]. While the algorithm performed quite well on certain evaluation metrics, the model was overly simplistic and failed to effectively capture the complex nonlinear relationships and multidimensional factors within the sales data, limiting its predictive capability in practical applications. The author [PERSON] used the XGBoost model, a LightGBM tree-based model, and a Long Short-Term Memory (LSTM) network for sales forecasting [3]. While these individual models showed reasonable performance on certain evaluation metrics, they failed to fully leverage the strengths of each model and struggled to effectively capture the complex nonlinear relationships and multidimensional factors within the sales data, limiting their predictive capability in real-world applications. [PERSON] et al. proposed a multi-step time-series forecasting method based on Informer, XGBoost, and Genetic Algorithm (GA) [4]. This method combines Informer with XGBoost and optimizes the model weights through GA to improve the accuracy and stability of multi-step time-series forecasting. However, it still faces significant challenges in handling long-term and mid-term data, especially regarding its sensitivity to long-term trend changes. These limitations affect the model's accuracy in handling complex multi-step time-series forecasts, thereby restricting its practical application in long-term prediction tasks. Existing forecasting models for FMCG sales often fail to effectively capture long-term dependencies and complex seasonal trends due to their reliance on simplistic feature extraction methods or limited temporal modeling capacity. While models like LSTM and Transformer show promise, they struggle to address multi-dimensional data and long-term trend variations, especially in dynamic markets. This research aims to fill this gap by proposing a novel hybrid approach, STL-DCSInformer-ETS, which integrates STL decomposition, DCSInformer, and ETS models to better capture both short-term fluctuations and long-term trends. This study first employs the RF-RFE method to quantitatively identify key features, enhancing feature selection precision and improving predictive performance and model reliability. Building on this, the study proposes an innovative hybrid model, STL-DCSInformer-ETS, combining STL decomposition, an enhanced DCSInformer model, and the ETS model. Compared to previous models, DCSInformer introduces novel capabilities, such as its ability to simultaneously capture both short-term fluctuations and long-term trends through dilated causal convolution and multi-scale feature extraction. This effectively addresses the shortcomings of traditional models, which struggle with long-term dependencies. The STL decomposition reduces data complexity by partitioning time-series data into trend, seasonal, and residual components, streamlining the forecasting process.