# GRU Neural Network Based on CEEMDAN-Wavelet for Stock Price Prediction
## 5 Discussion  
Figure 7c,f show plots of the actual versus predicted values of the model predicting future movements of the CSI and S&p500 data, respectively. Tables 1 and 2 show that the differential value between the denoised GRU and the non-denoised GRU is 0.008 and 0.019 in the \(R^{2}\) in CSI and S&P, respectively, and both \(R^{2}\) of denoised GRU reach above 0.99, which indicates that the denoised GRU model has a great advantage in the goodness of fit. Figure 7: (a) IMF components of CSI300; (b) denoised signal of CSI300; (c) forecast result of CSI300 (d) IMF components of S&P500; (e) denoised signal of S&P500; (f) forecast result of S&P500. In order to select the optimum model, we did ten experiments for the significance analysis test and obtained ten sets of _MSE_ and _MAE_ of the six models. Since the ten sets of _MSE_ and _MAE_ of ARIMA did not have any variation and the mean values were 769.69 and 19.32, which were significantly larger than GRU based on CEEMDAN-wavelet, we found GRU based on CEEMDAN-wavelet is better than ARIMA. In our study, GRU based on CEEMDAN-wavelet was used as the treatment group model. The LSTM, GRU, and CNN-BiLSTM are compared with GRU based on CEEMDAN-wavelet in turn in a two-by-two \(t\)-test, using as the experimental group models. We know that the p-value of the \(t\)-test is less than 0.05; in other words, there is a significant difference between the means of the values taken by the two models on this indicator. Tables 3 and 4 selected ten experiments of CSI300 to study the significance analysis of _MSE_ and _MAE_. The mean value of _MSE_ for GRU based on CEEMDAN-wavelet is 303.10 and the mean value of _MAE_ is 13.70. From Tables 3 and 4, it is concluded that the \(p\)-values of \(t\)-tests of GRU, CNN-BiLSTM, and ANN on _MSE_ and _MAE_ are less than 0.05, i.e., there is a significant difference in the mean values of these three models on _MSE_ and _MAE_. In addition, according to the mean values of _MSE_ and _MAE_ obtained by the ten experiments conducted, the mean values of _MSE_ and _MAE_ of GRU based on CEEMDAN-wavelet are the smallest; so, we conclude that GRU based on CEEMDAN-wavelet is superior to the other three models. For LSTM, even though its \(p\)-value of the \(t\)-test is larger than 0.05, since its mean values of _MSE_ and _MAE_ are larger than those of GRU based on CEEMDAN-wavelet, we conclude that GRU based on CEEMDAN-wavelet is superior to LSTM. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & _RMSE_ & _MSE_ & _R\({}^{2}\)_ & _MAE_ \\ \hline GRU based on & 12.99 & 168.89 & 0.994 & 10.63 \\ CEEMDAN–wavelet & LSTM & 18.14 & 329.06 & 0.98 & 15.15 \\ ARIMA & 49.376 & 2437.98 & 0.79 & 37.8 \\ GRU & 17.07 & 291.37 & 0.986 & 11.96 \\ CNN-BiLSTM & 20.14 & 405.62 & 0.91 & 13.68 \\ ANN & 22.47 & 504.90 & 0.87 & 14.59 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison between proposed network structure and other neural networks based on CSI300. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & _RMSE_ & _MSE_ & _R\({}^{2}\)_ & _MAE_ \\ \hline GRU based on & 22.27 & 496.07 & 0.991 & 17.39 \\ CEEMDAN–wavelet & LSTM & 26.34 & 693.79 & 0.97 & 16.544 \\ ARIMA & 27.74 & 769.68 & 0.94 & 19.32 \\ GRU & 23.51 & 552.99 & 0.97 & 21.23 \\ CNN-BiLSTM & 24.28 & 589.52 & 0.96 & 19.87 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison between proposed network structure and other neural networks based on S&P500. \begin{table}
\begin{tabular}{c c c c} \hline
**Control Model** & **Test Model** & _p Value of \(t\)-Test_ & **Mean Value** \\ \hline  & LSTM & 0.34 & 321.60 \\ GRU based on & GRU & 0.01 & 380.81 \\ CEEMDAN–wavelet (303.10) & CNN-BiLSTM & \(2.08\times 10^{-7}\) & 691.78 \\ ANN & \(2.51\times 10^{-6}\) & 526.46 \\ \hline \end{tabular}
\end{table} 
Table 3: The _MSE_ significance analysis based on CSI300. Similarly, Tables 5 and 6 represent the ten experiments of S&P500 to study the significance analysis of _MSE_ and _MAE_. The mean value of _MSE_ for GRU based on CEEMDAN-wavelet is 162.85 and the mean value of _MAE_ is 9.18.