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Long-term prediction of multivariate time series is still an important butchallenging problem. The key to solve this problem is to capture the spatialcorrelations at the same time, the spatio-temporal relationships at differenttimes and the long-term dependence of the temporal relationships betweendifferent series. Attention-based recurrent neural networks (RNN) caneffectively represent the dynamic spatio-temporal relationships betweenexogenous series and target series, but it only performs well in one-step timeprediction and short-term time prediction. In this paper, inspired by humanattention mechanism including the dual-stage two-phase (DSTP) model and theinfluence mechanism of target information and non-target information, wepropose DSTP-based RNN (DSTP-RNN) and DSTP-RNN-2 respectively for long-termtime series prediction. Specifically, we first propose the DSTP-based structureto enhance the spatial correlations between exogenous series. The first phaseproduces violent but decentralized response weight, while the second phaseleads to stationary and concentrated response weight. Secondly, we employmultiple attentions on target series to boost the long-term dependence.Finally, we study the performance of deep spatial attention mechanism andprovide experiment and interpretation. Our methods outperform nine baselinemethods on four datasets in the fields of energy, finance, environment andmedicine, respectively.

DSTP-RNN: a dual-stage two-phase attention-based recurrent neural networks for long-term and multivariate time series prediction