## 2 SCINet  
SCINet [17] is a hierarchical network that enhances the predictability of an original time series by capturing the time dependence of features at multiple time resolutions. SCINet has a binary tree structure, as shown in Figure 0(a). The basic component of SCINet is the SCI-Block, as shown in Figure 0(b). In each SCI-Block, the original sequence is decomposed into two sub-sequences. Different convolution modules extract homogeneous and heterogeneous information from the decomposed sub-sequences. Through interactive learning and information complementarity, new sequence representations are formed. To capture the dynamic features at different time granularities, SCINet downsamples the input sequence \(F\) in the time dimension to obtain \(F_{old}\) and \(F_{even}\). These two sub-sequences have a relatively coarse time resolution and retain most of the information of the original sequence. In each SCI-Block, four different convolution modules, namely \(\psi\), \(\phi\), \(\eta\), and \(\rho\), are employed to extract the features of \(F_{old}\) and \(F_{even}\). To deal with the potential information loss problem caused by downsampling, an interactive learning strategy is introduced in SCI-Block to facilitate the information exchange between subsequences. Firstly, \(F_{old}\) and \(F_{even}\) are mapped to the hidden layer states through two convolution modules, \(\psi\) and \(\phi\). This stage can be regarded as performing scaling transformations on \(F_{old}\) a \(F_{even}\), as in Formula (1). Then, using the other two convolution modules \(\eta\) and \(\rho\), the scaled features after the first stage are further mapped and interacted to obtain two updated features, \(F_{old}^{\prime}\) and \(F_{even}^{\prime}\), as shown in Formula (2).  
\[F_{even}^{s} =F_{even}\odot exp(\psi(F_{old})), \tag{1}\] \[F_{old}^{s} =F_{odd}\odot exp(\phi(F_{even}))\] (2) \[F_{even}^{\prime} =F_{even}^{s}-\eta\left(F_{odd}^{s}\right),\] (3) \[F_{odd}^{\prime} =F_{odd}^{s}+\rho\left(F_{even}^{s}\right), \tag{4}\]where \(\psi\), \(\phi\), \(\eta\), and \(\rho\) are convolutional filters, and _exp_ is the exponential transformation.  
The input data can be divided into \(k\) (\(k=1,2,\ldots\), \(K\)) time sequence; \(X_{\text{seq}}=\left[X^{1},\ X^{2},\ \ldots,\ X^{K}\right]\). For each time sequence, \(X^{k}=\left[x_{1}^{k},\ x_{2}^{k},\ \ldots,\ x_{T}^{k}\right]\), where \(T\) is the window length, is decomposed layer by layer, and is processed by different levels of SCI-Blocks, which can effectively learn the features at different temporal resolutions. Feature information from previous layers is accumulated, meaning deeper layers contain information from time-scale features at shallower layers. The concatenated features are accumulated with the original sequence \(X_{\text{seq}}\) to obtain the hidden layer dynamic features, \(\mathbf{h}\mathbf{v}\). The \(\mathbf{h}\mathbf{v}\) is fed to the fully connected layer for decoding to obtain the predicted sequence \(\hat{X}^{k}=\left[\hat{x}_{1}^{k},\ \hat{x}_{2}^{k},\ \ldots,\ \hat{x}_{\tau}^{k}\right]\), where \(\tau\) is the step length of the refined sequence. Then, the absolute error loss function between the predicted value and the true value is given as follows:  
\[Loss=\frac{1}{\tau}\sum\limits_{i=1}^{\tau}\|\hat{x}_{i}^{\tau}-x_{i}^{\tau}\| \tag{3}\]