## 2 Related Work
### Time-Series Forecasting with Transformer Structure  
Recently, transformer architectures have made tremendous progress in the field of natural language processing, which has become a new mainstream research paradigm. Considering the similar characteristics of time-series data and text data in the sequential relationship, many scholars have introduced the transformer structure to leverage the time-series forecasting methods with diverse optimized recurrent neural networks [26; 27].  
[PERSON] [28] considered each variable as an independent variates token and constructed the iTransformer model with the multi-head self-attention mechanism, thus effectively capturing the complex collaborative relationship between variables in multivariate time series and improving the modeling ability of multivariate information. Borrowing the idea of patch embedding in image processing, [PERSON] [29] divided the time series into patches of fixed length and proposed the PatchIST model, which better extracts global dependencies while preserving local features and effectively alleviates the problem of capturing long-distance dependencies in the time dimension. [PERSON] [30] proposed Crossformer, which constructs a dual-channel attention mechanism, namely the time channel and variable channel, to adaptively learn the cross-dependencies between time points and variables. The ability to model the interaction between variables is enhanced. [PERSON] [31] developed a time-series modeling method called TiDE, which decomposes the series into trend and seasonal components and models them separately using the attention mechanism. It significantly improves the stability and accuracy of the model in long-term prediction scenarios. [PERSON] [32] innovatively introduced 2D temporal modeling structures that not only model the temporal dimension of time series but also introduce 2D convolution operations across time periods, thus capturing complex nonlinear temporal evolution patterns. [PERSON] [33] proposed SCINet, using a learnable Sample Convolution Interaction module. This structure allows the model to learn the nonlinear interaction between different time steps and performs efficient time modeling by layer-by-layer convolution. [PERSON] [34] enhances the transformer model by incorporating frequency decomposition. The time series is projected into the frequency domain, and then the frequency components are modeled by self-attention, which allows the model to capture both short-term and long-term dependencies in time-series data. [PERSON] [35] introduced a stationarity enhancement module to make the dynamic characteristics of time series more stationary through an adaptive transformation mechanism, aiming at the difficulty of modeling non-stationary time series. [PERSON] [36] introduced the auto-correlation mechanism to mine the periodicity and trend in time series. This method achieved leading performance in multiple prediction tasks through stacked decomposition modules and reconstruction mechanisms.  
The transformer structure utilizes the attention mechanism to capture the potential correlation of dynamic time series and then makes predictions for the next time steps, instead of the conventional recurrent neural network structure. However, the model exhibits limited capacity for long-term dependency capture and is unable to provide accurate predictions over extended periods.  
To address this limitation, the proposed TSNN-ESTD utilizes a short-term predictor based on iTransformer, optimistically strengthens long-term modeling, and introduces a bias-correction strategy that combines short-term outputs to calibrate long-term predictions. This design improves stability, reduces cumulative error, and significantly alleviates prediction bias in long-term scenarios.