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Time series forecasting is prevalent in various real-world applications.Despite the promising results of deep learning models in time seriesforecasting, especially the Recurrent Neural Networks (RNNs), the explanationsof time series models, which are critical in high-stakes applications, havereceived little attention. In this paper, we propose a Decomposition-basedLinear Explainable LSTM (DeLELSTM) to improve the interpretability of LSTM.Conventionally, the interpretability of RNNs only concentrates on the variableimportance and time importance. We additionally distinguish between theinstantaneous influence of new coming data and the long-term effects ofhistorical data. Specifically, DeLELSTM consists of two components, i.e.,standard LSTM and tensorized LSTM. The tensorized LSTM assigns each variablewith a unique hidden state making up a matrix $\mathbf{h}_t$, and the standardLSTM models all the variables with a shared hidden state $\mathbf{H}_t$. Bydecomposing the $\mathbf{H}_t$ into the linear combination of past information$\mathbf{h}_{t-1}$ and the fresh information $\mathbf{h}_{t}-\mathbf{h}_{t-1}$,we can get the instantaneous influence and the long-term effect of eachvariable. In addition, the advantage of linear regression also makes theexplanation transparent and clear. We demonstrate the effectiveness andinterpretability of DeLELSTM on three empirical datasets. Extensive experimentsshow that the proposed method achieves competitive performance against thebaseline methods and provides a reliable explanation relative to domainknowledge.

DeLELSTM: Decomposition-based Linear Explainable LSTM to Capture Instantaneous and Long-term Effects in Time Series