## 5 Conclusions  
The main objective of this study was to surmount the constraints imposed by stationarity and linearity by employing nonlinear autoregressive (NAR) models in tandem with error correction through support vector regression (SVR). The results presented herein unequivocally demonstrate the enhanced performance of the proposed NAR-SVR hybrid model in comparison to various other machine learning (ML) models, including NAR, SVR, and LSTM, as well as established methodologies like ARIMA, which have proven efficient in addressing univariate time series data. Furthermore, the comparative analysis undertaken among different ML models when applied to the same time series dataset substantiates the undeniable superiority of our innovative approach. By transcending these traditional limitations, our hybrid methodology introduces an avant-garde paradigm for univariate time series forecasting, thus advancing the state of the art in this field. Notably, the inherent simplicity of our model's implementation is a commendable attribute. The requirement for a singular source of information, namely, the historical data series of the variable, contributes to its ease of deployment. In addition, the computational overhead associated with our approach remains significantly lower than that of other intricate ML algorithms, further highlighting the practical feasibility and efficiency of our proposed model. In summation, the amalgamation of NAR models with SVR-based error correction culminates in a powerful forecasting algorithm that not only overcomes established limitations but also offers a streamlined implementation and computational advantage. As such, our research contributes a valuable addition to the arsenal of techniques available for univariate time series analysis and prediction. In light of the multitude of available ML models, such as LSTM, it is important to clarify that our current endeavor does not aim to undertake a direct comparison with these alternatives. Rather, our focus centers on our proposed approach. Acknowledging this contextual limitation not only elevates the transparency and credibility of our research, but also illuminates a promising avenue for subsequent investigations in this evolving domain. In conclusion, our study showcases the utility of combining nonlinear autoregressive neural networks with cutting-edge machine learning SVR for optimizing time series forecasting. The promising results obtained across various univariate datasets support the effectiveness of our proposed model, positioning it as a superior option for making accurate predictions on different types of time series. Nonetheless, future research should focus on incorporating exogenous variables and exploring alternative learning rules to further enhance the capabilities of our approach. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Our NAR-SVR** & **[68]** \\ \hline COVID-19 in Spain & 673.28 & 696.35 \\ COVID-19 in Italy & 325.11 & 566.88 \\ COVID-19 in Turkey & 204.57 & 1892.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE value comparison, 14 May 2020/28 May 2020. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Our** & & [72] & \\ \hline SARS-CoV-2 & NAR–SVR & ARIMA & LSTM (single feature) & LSTM (multifeature) \\ RMSE & 195.03 & 209.26 & 198.45 & 197.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RMSE value comparison, 1 May 2018/10 November 2018. **Author Contributions:** Conceptualization, J.D.B. ; methodology, J.D.B. and J.M. ; validation, J.D.B. and J.M. ; investigation, J.D.B. and J.M. ; resources, J.D.B. ; data curation, J.M. ; writing--original draft preparation, J.D.B. and J.M. ; writing--review and editing, J.D.B. ; project administration, J.D.B. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Data Availability Statement:** Restrictions apply to the availability of these data. Data were obtained from a third party. The data are not publicly available due to privacy.