ADMS-LSTM: A multi-scale stacked LSTMs long-term prediction method based on an adaptive decomposition framework with DFT-AutoCorrelation

Effective long-term forecasting can provide valuable decision-making information and demonstrate significant application value. Because of the difficulty of learning complex time patterns and the accumulation of prediction errors, the current research on long-term forecasting is still limited. In this paper, to capture multi-scale long-term dependencies, a novel framework Discrete Fourier Transform (DFT)-AutoCorrelation Pyramid Decomposition LSTM (ADMS-LSTM) is proposed. ADMS-LSTM mainly includes an adaptive decomposition window analysis module, a pyramid decomposition module, and a prediction-fusion module. First, the adaptive decomposition window analysis module based on DFT and the AutoCorrelation mechanism is designed to select the optimal decomposition window adaptively and provide a reliable theoretical basis for the pyramid decomposition module. Furthermore, multi-scaled information from the pyramid decomposition module is beneficial for mining distant historical dependencies. Finally, in the prediction-fusion module, the complex time patterns are learned and multi-scaled prediction series are fused, to improve the local prediction information and solve the problem of prediction error accumulation. To verify the effectiveness and robustness of the proposed method, six publicly available benchmark datasets are chosen for our experiment. Comparative experimental results show that our proposed method achieves state-of-the-art performance on these datasets compared with other latest methods. The proposed method can effectively alleviate the problem of error accumulation, extract the long-term temporal characteristics, and obtain excellent long-term prediction results. To the best of our knowledge, this is the first work based on rigorous mathematical theory to adaptively select decomposition windows for long-sequence information learning.