## 1 Introduction  
Time-series data consists of sequences of random variables organized in chronological order, reflecting the changes in a specific entity, phenomenon, or process over time. Examples of time-series data include hourly temperature readings, daily stock closing prices, and monthly sales figures.  
Time-series forecasting leverages the inherent patterns within time-series data by establishing an appropriate mathematical model to estimate and predict the values of the series at specific future points or intervals. Recently, time-series forecasting has become an important branch of data science, which aims to find out the inherent regularity by analyzing historical time-series data and then predict the future development trend. It has attracted the attention of both academia and industry in the process of digital and intelligent transformation, especially in meteorology, transportation, finance, and other industries. Diverse time-series models have been developed to deal with weather forecasting, traffic flow prediction, quantitative decision-making, etc.  
Recently, numerous scholars have sought to enhance the performance of conventional time-series forecasting models through various techniques like autoregression, recurrent neural networks, Long Short-Term Memory (LSTM), etc. Transformer, as the mainstream technique, was widely introduced by the frontier models, for example, iTransformer, PatchTST, Crossformer, and Autoformer. These transformer-based models significantly improve the ability of multivariate time-series data modeling and achieve state-of the-art performance.  
However, the performance is often unsatisfactory when faced with long-term forecasting scenarios. The bias between the predicted value and ground truth is usually within expectation in the short-term scenario but shows an obvious linear growth trend as the forecast period grows. Therefore, improving the awareness and prediction ability of time-series models for long-term scenarios has emerged as a crucial issue.  
To facilitate this line of research, we innovatively propose the Time-Series Neural Networks via Ensemble of Short-Term Dependencies (TSNN-ESTD) to fill the gaps of the off-the-shelf model in long-term prediction scenarios. TSNN-ESTD mainly focuses on mitigating the long-term forecasting bias of long-term predictions through hybrid ensemble strategies.  
TSNN-ESTD takes iTransformer as the base predictor to train the short-term and long-term prediction models at the same time. Considering the limitations of the linear decoding layer in the vanilla iTransformer, we optimize the decoder layer as the LSTM and additionally train another long-term model for enhancing stability. The short-term prediction results are replicated in multiple copies to ensure the consistency of the output dimension. Then, we design the ensemble strategy that uses the short-term prediction results to correct the prediction bias of the long-term model. In this situation, TSNN-ESTD enhances the iTransformer by substituting its linear decoding layer with an LSTM layer and incorporating an additional long-term forecasting model to ensure stability. A hybrid ensemble method is employed to integrate short-term and long-term predictions, thereby mitigating bias in long-term forecasts.  
The main contributions of this paper can be summarized as follows:  
1. We investigate the efficacy of numerous existing methodologies in both short-term and long-term forecasting and construct a general ensemble learning framework for multivariate time-series forecasting.
2. We optimize the decoding layer structure of iTransformer by modifying the MLP to an LSTM layer to improve the ability of long-term dependencies.
3. We explore the ensemble strategy of multiple base predictors with different scales to mitigate the long-term forecasting bias in time-series neural networks with short-term dependencies.
4. Extensive experiments have been conducted to demonstrate the superiority of our proposal.