## 4 Implementation and Discussion of Results
### Selecting the ARIMA Parameters
#### 4.3.1 Building, Training, and Testing the ARIMA Model  
By fitting the training dataset, the ARIMA method is used to predict the number of new confirmed, recovered, and mortality cases on the test dataset. This section describes the ARIMA model's forecasting findings for future COVID-19 cases. The dataset is split into training and testing, and the test dataset's forecast and actual values are reported. With the forecasted confirmed, dead, and recovered cases using the ARIMA model, good forecasting  
Figure 6: Prediction over a 60-day forecast for the recovered cases using the LSTM model.  
Figure 7: Prediction over a 60-day forecast for the mortality cases using the LSTM model.  
efficiency and precision are attained. We summarize the different values of the error metrics in Table 2. From Table 2, the MAPE values of the confirmed, dead, and recovered cases for the ARIMA model were found to be 21.4%, 16.27%, and 34.98%, respectively. By further looking at the six error measures of the ARIMA model, it can be observed that ARIMA has excellent performance in predicting the death cases, but poor performance for confirmed and recovered cases. For example, ARIMA's nRMSE and \(R^{2}\) values for predicting the number of death cases are 7.0% and 0.88, respectively. For the confirmed cases, the values of the nRMSE and \(R^{2}\) are 13.7% and 0.15, respectively, while for recovered they are 10.05% and 0.39, respectively. The scatter plots that compare the actual and the predicted values of the three cases on the testing sets can be seen in Figures 8-10.  
As we see in the scatter plot, the predicted confirmed cases show some higher-order polynomial relationship, rather than the first-order linear relationship with the actual confirmed cases. The regression line in the plot, which has been drawn assuming a linear relationship and placed in the plot for comparison with other similar plots, is therefore not valid.  
As in the performance in confirmed cases, ARIMA prediction of recovered cases shows some non-linear function relationship with the actual cases. When the number of cases is around 1000 with small differences, ARIMA made predictions of a large range from 1000 to 1800. On the other hand, for actual cases from about 1100 to about 5000, ARIMA makes an almost constant prediction of about 1800 to 1900, making the overall scatter plot a stage-wise appearance.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Predicted Variable** & **RMSE** & **nRMSE** & **MAE** & **nMAE** & **MAPE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{3}{*}{ARIMA} & Confirmed & 578.1 & 13.7 & 258.6 & 6.1 & 21.4 & 0.15 \\  & Deaths & 3.6 & 7.0 & 2.25 & 4.33 & 16.27 & 0.88 \\  & Recovered & 473.48 & 10.05 & 248.62 & 5.28 & 34.98 & 0.39 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance evaluation of the test dataset forecasting using the ARIMA model.  
Figure 8: A scatter plot of the confirmed cases by ARIMA on the testing dataset.  
In contrast to the performances in confirmed and recovered cases, ARIMA's predictions in the mortality cases are very good, finally managing to establish a linear relationship between the actual cases and predicted cases. Also, the points in the scatter plot closely follow the regression line for the number of cases up to 30, before starting to show performance deterioration for the number of mortality cases beyond 30.