# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 5 Experimental Procedures
### Assessment of Experiment Result of Other Methods
#### 5.2.5 Kr  
Kernel ridge regression (KR) integrates ridge regression with kernel methods, utilizing L2 norm regularization to obtain linear least squares. In the linear kernel's data space, it mirrors a linear mathematical operation from the initial space. Conversely, with a nonlinear kernel, it mirrors a nonlinear mathematical operation from the initial space. This approach combines the regularization benefits of ridge regression with the flexibility of kernel methods, enabling the effective modeling of both linear and nonlinear relationships in the data. Table 3 exhibits the forecast results of nine methodologies applied to two time series: sine and temperature. Each approach utilizes data processed from these two series, with the specific data length being detailed in the third row of Table 1. The objective was to predict the subsequent time-series value by analyzing the preceding 11 consecutive values. The evaluation in Table 3 is based on the R\({}^{2}\), MAE, and RMSE, comparing the projected values against the actual outcomes. Lower RMSE and MAE values signify a stronger predictive capability, while a higher R\({}^{2}\) score indicates a greater prediction accuracy of the employed method. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Method** & **Sin** & **Temperature** \\ \hline \multirow{4}{*}{RFR} & RMSE & 0.005341 & 1.464543 \\  & MAE & 0.003571 & 1.058784 \\  & R\({}^{2}\) & 0.999970 & 0.977853 \\  & RMSE & 0.011126 & 1.885286 \\  & MAE & 0.005177 & 1.419670 \\  & R\({}^{2}\) & 0.999869 & 0.963300 \\  & RMSE & 0.033481 & 3.207245 \\  & MAE & 0.030063 & 2.692735 \\  & R\({}^{2}\) & 0.998818 & 0.893789 \\  & RMSE & 0.012665 & 1.419190 \\ GBR & MAE & 0.009983 & 0.998826 \\  & R\({}^{2}\) & 0.999831 & 0.979204 \\  & RMSE & 0.838632 & 8.860991 \\ KR & MAE & 0.700675 & 7.788972 \\  & R\({}^{2}\) & 0.258231 & 0.189280 \\  & RMSE & 0.650849 & 8.455165 \\ LSTM & MAE & 0.042390 & 1.545091 \\  & R\({}^{2}\) & 0.836532 & 0.682006 \\  & RMSE & 0.389935 & 3.030954 \\ EEMD-LSTM & MAE & 0.038895 & 0.922435 \\  & R\({}^{2}\) & 0.854381 & 0.738811 \\  & RMSE & 0.000035 & 1.392644 \\ LR & MAE & 0.000022 & 0.978153 \\  & R\({}^{2}\) & 0.999985 & 0.979974 \\  & RMSE & 0.000027 & 0.713150 \\ Proposed & MAE & 0.000021 & 0.512700 \\ EEMD-LR & R\({}^{2}\) & 1.000000 & 0.994749 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Forecasting outcomes from nine approaches for two data sets. EEMD-LSTM and LSTM are both greater than 0.03 but less than 0.07, which indicates that they have rather average predictive accuracy but significantly poorer performance compared to LR and EEMD-LR. Notably, these five methods excel in forecasting sequences with consistent fluctuations. Figure 13 illustrates the prediction performance of the LR method. The overall predictive efficacy of the LR method is commendable, which is particularly evident when the method is used to forecast 800 consecutive data points. For clarity, only the forecasted results for the 800 successive data points are depicted in the diagrams presented herein. From Table 3, it is evident that LSTM, EEMD-LSTM, and NuSVR yield notably high MAE and RMSE values for the temperature data, which indicates their poor predictive performance in this regard. Conversely, while NuSVR exhibits relatively high RMSE and MAE values for the sine data, LSTM and EEMD-LSTM do not demonstrate significant discrepancies in this aspect. This suggests that NuSVR, EEMD-LSTM, and LSTM are better suited for forecasting sequences with regular and stable patterns, whereas they may not be as effective for sequences with irregular patterns, as evidenced by the more predictable and stable nature of the sine data. Upon careful examination of Table 3, it is evident that, although the KR, LSTM, and EEMD-LSTM methods did not, the other five methods demonstrate a favorable predictive performance for sine time-series data. The R2 evaluation index for these five methods exceeds 0.98, which indicates their superior predictive capability for time series that exhibit regular and stable patterns.