## 3 Methodological Background  
In order to better express our problem, we declare some symbols in advance. In particular, we use bold capital letters (e.g., \(\mathbf{X}\)), bold lowercase letters (e.g., \(\mathbf{x}\)), lowercase (e.g., \(x\)), and Greek letters (e.g., \(\alpha\)) to denote matrices, vectors, scalar, and model hyperparameters, respectively. Denote by \(\mathbf{X}=[\mathbf{x}_{1},\mathbf{x}_{2},\mathbf{x}_{3},\cdots,\mathbf{x}_{n}]^{\top}\in\mathbb{R }^{u\times d}\) an input time series, where \(u\) is the length of the time series, and \(\mathbf{x}_{t}\) is a \(d\)-dimensional feature vector at the \(t\)-th time step. In this paper, the objective was to forecast the movement direction of time series at the next time step \(u+1\).  
In time series analysis, moving average indicators are one of the most favored tools to measure the overall changing patterns of time series. Typically, there are three traditional moving average indicators frequently used in real scenarios, including simple moving average (SMA) [41], exponential moving average (EMA) [42], and weighted moving average (WMA) [43].  
The SMA indicator calculates an average of time series data during a past period. Specifically, the SMA indicator at the \(t\)-th time step with a lookback window size of \(l\) can be calculated as  
\[\text{SMA}_{l}^{t}=\frac{\sum_{i=1}^{l}p_{t-i+1}}{l}, \tag{1}\]  
where \(p_{i}\) is the data of the \(i\)-th time step. Intuitively, the SMA indicator is an effective means to eliminate the strong fluctuations of time series. However, it equally treats the data at each time step and ignores the subtle differences of their importance.  
As a step further, the EMA indicator adopts an exponential decline manner to weigh the time series data. Particularly, it gives greater weights to recent data than past ones, and can be recursively computed as  
\[\text{EMA}_{l}^{t}=\alpha\times(p_{t}-EMA_{l}^{t-1})+EMA_{l}^{t-1}, \tag{2}\]  
where \(\alpha=\frac{2}{t+1}\in(0,1)\) represents a degree of weight reduction.  
The WMA indicator works in a similar way to EMA but uses the predefined data weights, meaning that:  
\[\text{WMA}_{l}^{t}=\frac{\sum_{i=1}^{l}p_{t-i+1}w_{i}}{\sum_{i=1}^{l}w_{i}}, \tag{3}\]  
where \(w_{i}\) denotes the predefined weight. For notational simplicity, we shall omit the superscript \(t\) in the following.  
In time series analysis, it is widely believed that the intersection of moving average indicators at different scales suggests a certain trend signal [44]. For example, when a short-term moving average crosses a long-term moving average from bottom to top, it means that an upward signal of a time series can be generated. On the contrary, if a short-term moving average crosses a long-term moving average from top to bottom, a downward time series trend may be predicted. However, such a strategy is mainly formed on humans' subjective experience, and may not be applicable to different time series.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Related Work** \\ \hline Statistical model & [13; 14; 15; 16; 37; 38; 39; 40] \\ Traditional machine learning model & [17; 18; 19; 20; 21] \\ Deep RNN model & [4; 23; 24; 25; 26; 31; 32; 33] \\ Deep self-attention model & [27; 28; 29; 30] \\ \hline \hline \end{tabular}
\end{table}
Table 1: A brief summary of related work.