Long-term prediction of multivariate time series is still an important but challenging problem. The key to solve this problem is to capture the spatial correlations at the same time, the spatio-temporal relationships at different times and the long-term dependence of the temporal relationships between different series. Attention-based recurrent neural networks (RNN) can effectively represent the dynamic spatio-temporal relationships between exogenous series and target series, but it only performs well in one-step time prediction and short-term time prediction. In this paper, inspired by human attention mechanism including the dual-stage two-phase (DSTP) model and the influence mechanism of target information and non-target information, we propose DSTP-based RNN (DSTP-RNN) and DSTP-RNN-2 respectively for long-term time series prediction. Specifically, we first propose the DSTP-based structure to enhance the spatial correlations between exogenous series. The first phase produces violent but decentralized response weight, while the second phase leads to stationary and concentrated response weight. Secondly, we employ multiple attentions on target series to boost the long-term dependence. Finally, we study the performance of deep spatial attention mechanism and provide experiment and interpretation. Our methods outperform nine baseline methods on four datasets in the fields of energy, finance, environment and medicine, respectively.
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