## 6 Result and Discuss
### Data Prediction Performance Analysis
#### 6.2.2 Prediction Parameter Analysis  
In time series analysis and prediction, the mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) can calculate the deviation between the predicted value and the original value. The larger the deviation, the larger the MAE, MSE, and RMSE; the smaller the deviation, the smaller the MAE, MSE, and RMSE. Therefore, the MAE, MSE, and RMSE are often used to evaluate the performance of prediction algorithms [54]. Among these, the MAE is defined as shown in [54]:  
\[\text{MAE}=\frac{1}{N}\sum\
olimits_{x=1}^{N}\left|p_{x}-\hat{p}_{x}\right|\,, \tag{22}\]  
The MSE is defined as shown in [54]:  
\[\text{MSE}=\frac{1}{N}\sum\
olimits_{x=1}^{N}(p_{x}-\hat{p}_{x})^{2}, \tag{23}\]  
The RMSE is defined as shown in [54]:  
\[\text{RMSE}=\sqrt{\frac{1}{N}\sum\
olimits_{x=1}^{N}(p_{x}-\hat{p}_{x})^{2}}, \tag{24}\]  
where, the monitoring data are denoted by \(p_{x}\), the forecast data are denoted by \(\hat{p}_{x}\), the length of the data series is denoted by \(N\), and \(x\) denotes the label of the data series.  
Using the 40-day (960 h) temperature data in the four periods, ARMA models with different (p, d, q) parameters were selected to predict the data of the next day (24 h). The MAE, MSE, and RMSE curves calculated using the predicted data and the original monitoring data are shown in Figure 10.  
Figure 9: Comparison of ARMA and EP-ARMA algorithm prediction data and original monitoring data in different periods. Figures (**a**,**c**,**e**,**g**) in the left part reflect the comparison between the original monitoring data and ARMA prediction data in the periods (0, 960), (960, 1920), (1920, 2880), and (2880, 3840), and in the next 24 h period. Figures (**b**,**d**,**f**,**h**) in the right part reflect the comparison between the original monitoring data and EP-ARMA (0.1) correction data in the periods (0, 960), (960, 1920), (1920, 2880), and (2880, 3840), and in the next 24 h period.  
Figure 10 shows that the curves of MAE, MSE and RMSE vary sharply with different (p, d, q) configurations. The curves in different periods show that the selection of different (p, d, q) values has an important impact on the prediction performance of EP-ARMA. The (p, d, q) configuration with the highest prediction accuracy is not completely consistent in different periods. Therefore, high-precision EP-ARMA prediction cannot be achieved with a fixed (p, d, q) configuration. It is necessary to find a new (p, d, q) configuration through the automatic parameter-matching method after a period of time, to ensure the stability of the predictive performance.  
Figure 10 also shows that, due to the stability of the underwater temperature data, it is not necessary to change the (p, d, q) every period. The parameters in multiple consecutive periods do not change to a large extent. Therefore, it is only necessary to dynamically adjust the parameter of (p, d, q) when the prediction performance is greatly reduced. In the case of poor transmission conditions or stable changes in monitoring data, the data updating frequency can be reduced or even stopped. The subsequent data can be generated using EP-ARMA and historical data based on the (p, d, q) in the previous period, which can greatly improve the data transmission efficiency of the EP-ADTA.