EMD-based combined attention mechanism RNN for multivariate time series forecasting

The Dual-stage Attention-based Recurrent Neural Network (DA-RNN) is a high-performance model for single-step multivariate time series prediction. By leveraging the encoder-decoder framework and additive attention, it effectively captures long-term temporal dependence. However, a critical limitation remains, i.e., it cannot simultaneously capture both long-term temporal dependencies and cross-timestamp inter-series interaction information. To address this gap, this paper proposes a dual-stage recurrent neural network integrated with a Combined Attention Mechanism (CAM). This novel CAM fuses additive attention, self-attention, and temporal pattern attention, which not only enhances the feature extraction capability of CNNs but also optimizes the structural coherence of decoder outputs. In the encoder module, CAM first selects driving sequences based on previous hidden states and then captures inter-series correlation information; the updated hidden state matrix is subsequently fed into the decoder. In the decoder module, CAM selectively focuses on relevant hidden states across different timestamps, updates context vectors by exploiting their intrinsic correlations for prediction, and incorporates an autoregressive module to further enhance the model’s robustness. Additionally, empirical mode decomposition (EMD) is employed for preprocessing the input time series, enabling the extraction of multi-frequency components. This integration forms a unified EMD-Attention-RNN framework, which effectively suppresses noise interference and improves the model’s interpretability. Experimental results on the SML2010 and NASDAQ 100 Stock datasets, coupled with rigorous statistical analysis, demonstrate that the proposed EMD-CAM-RNN outperforms existing state-of-the-art methods for multivariate time series forecasting.