TFFS: A trainable federal fusion strategy for multistep time series forecasting

This paper presents a trainable federal fusion strategy (TFFS) for multistep time series forecasting (MSTSF) that unifies the current strategies. First, we designed a feature fusion embedding scheme (FFES) that integrates sharing features and all future steps in a trainable mode to overcome the drawback of cumulative errors. Second, multitask learning was designed to train each step in a parallel mode, enabling each step to share a common feature with the others while keeping each step's personality. Finally, a multiple-input multiple-output scheme (MIMOS) was developed to forecast future step values in semi-series mode, which increases the flexibility. Owing to this design, TFFS provides the following advantages for MSTSF: 1) TFFS is free of cumulative errors in future horizons during training. 2) TFFS provides accurate multistep forecasting results, requiring only one model training. 3) Sharing common features while retaining each step's personality increases forecasting accuracy. We conducted many experiments on univariate and multivariate time-series datasets to validate the effectiveness of TFFS with seven common deep learning structures. The experimental results confirmed the state-of-the-art performance of the proposed method. Additionally, we extensively and systematically compared each strategy for MSTSF with deep learning.