## 5 Discussion and Conclusions  
### Comparison with Other Prediction Methods  
There are a variety of prediction methods existing in the literature; typical methods are, for example, ARIMA [50], Seasonal ARIMA [51], SVR [52], and LSTM [53]. Table 7 illustrates the advantages and disadvantages of these existing prediction methods. This paper then compares the performance of the proposed GRU-LightGBM method and the existing methods; see Figure 10. The comparison shows that the GRU-LightGBM model proposed in this paper is significantly superior to the other compared methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Advantages** & **Disadvantages** \\ \hline ARIMA & \begin{tabular}{c} Performs well in short-term prediction. \\ Only the prior data are needed. \\ \end{tabular} & \begin{tabular}{c} Cannot capture the nonlinear \\ relationships in sales. \\ \end{tabular} \\ \hline Seasonal ARIMA & \begin{tabular}{c} SARIMA is a type of ARIMA model that performs \\ well when dealing with seasonally affected time \\ series data. \\ \end{tabular} & \begin{tabular}{c} There are shortcomings in dealing with \\ time series that have periodicity. \\ \end{tabular} \\ \hline SVR & \begin{tabular}{c} SVR can execute linear and nonlinear regressions \\ with a high degree of accuracy by utilizing various \\ kernel functions [54]. \\ \end{tabular} & \begin{tabular}{c} Poor interpretation can be found when \\ solving nonlinear problems. \\ Weak in handling large datasets. \\ \end{tabular} \\ \hline LightGBM & \begin{tabular}{c} LightGBM is efficient and robust. \\ \end{tabular} & \begin{tabular}{c} The accuracy of prediction is inferior to \\ that of deep learning methods such as \\ LSTM and GRU. \\ \end{tabular} \\ \hline LSTM & \
\begin{tabular}{c} LSTM is addressed to tackle the problem of \\ gradient vanishing and explosion in the process of \\ long sequence calculation and has the capacity for \\ long-term memory [55]. \\ \end{tabular} & It has a slow training speed. \\ GRU &
\begin{tabular}{c} Same as LSTM. GRU is the lightweight \\ implementation of LSTM. \\ \end{tabular} & It has a slow training speed. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The comparison among different prediction methods. Figure 9: Sales prediction output (The prediction output of December is shown in the orange square region). The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are also used to analyze the prediction performance [56] among the above methods; see Equations (9)-(11). _RMSE_ reflects the degree of dispersion of the sample. _MAE_ reflects the true error. _MAPE_ is a measure of relative error, with an _MAPE_ value closer to 0 representing a more perfect model. The _RMSE_, _MAE_ and _MAPE_ evaluations among different prediction methods are shown in Table 8.  
\[RMSE=\sqrt{\frac{1}{m}{\sum_{i=1}^{m}(y_{i}-\hat{y}_{i})^{2}}} \tag{9}\]  
\[MAE=\frac{1}{m}{\sum_{i=1}^{m}}|y_{i}-\hat{y}_{i}| \tag{10}\]  
\[MAPE=\frac{100\%}{m}{\sum_{i=1}^{m}}\left|\frac{y_{i}-\hat{y}_{i}}{y_{i}}\right| \tag{11}\]  
where \(m\) represents the total size of the test set, \(y_{i}\) represents the true value and \(\hat{y}_{i}\) represents the prediction value. The comparison results indicate that the GRU-LightGBM model has the highest prediction accuracy among the compared models. The _RMSE_ and _MAE_ values of the GRU-LightGBM model are 8.01 and 5.41, respectively, which are significantly lower than those of the other compared models; for example, the best single model prediction method is GRU and the results are 11.19 in _RMSE_ and 8.76 in _MAE_. GRU-LightGBM also has the lowest _MAPE_ value, which indicates that it is the most perfect model. The _MAPE_ value of GRU-LightGBM is 4.11%; in comparison, for the prediction using a single model method,