## 5 Conclusions  
An improved tool for forecasting ozone concentration has been proposed using hybrid combinations of time series models in four districts of Metropolitan Lima between the years 2017 and 2019. It was shown that the combination of the models through the decomposition of the series ozone temporal data into \"long-term trend\", \"seasonal\", and \"stochastic\" series, by the use of the seasonal trend decomposition method, produced efficient model performance. The combinations made of the autoregressive models, nonlinear autoregressive models, and autoregressive moving average models generated 27 combinations for each sampling station. They demonstrated significant forecasts of the sample based on highly accurate and efficient descriptive, statistical, and graphic analysis tests, as a lower mean error occurred in the optimized forecast models compared to traditional models. Thus, the best hybrid models for the ATE (\({}^{\textbf{a}}\)STLD\({}^{\textbf{b}}_{\textbf{c}}\)), CDM (\({}^{\textbf{b}}\)STLD\({}^{\textbf{c}}_{\textbf{c}}\)), SB (\({}^{\textbf{b}}\)STLD\({}^{\textbf{c}}_{\textbf{c}}\)), and Santa Anita (\({}^{\textbf{c}}\)STLD\({}^{\textbf{c}}_{\textbf{c}}\)) stations were presented because they showed the best forecast reflected in the measurement of RMSE, RMSPE, MAE, MAPE, and CC, which were very small compared to the other models. The confirmation of the best models was statistically significant (\(p<0.05\)), being superior to the other models. The graphical representation of the mean errors (RMSE, RMSPE, MAE, MAPE, and CC) for the twenty-seven models at each sampling station presented a better precision for the supermodels compared to the rest of all the models combined. These statistical tests and graphical results show that the proposed forecast methodology is highly accurate and efficient in predicting hourly ozone concentration, which meant that the independent AR, NPAR, and ARIMA models were outperformed by our best models (\(p<0.05\)). The main drawback of this study is that it only provides hourly data on ozone concentration. It can be extended to include additional exogenous factors such as wind speed, temperature, wind direction, and humidity, which may improve the short-term forecast of ozone concentration. In addition, the current work uses only four district datasets in Lima, Peru. This can be extended to other districts of Lima (San Juan de Lurigancho, Chorrillos, Comas, San Juan de Miraflores, etc.) or to different regions of Peru (Huanuco, Coyahique, Traiguen, Padre Las Casas, Santiago, etc.). It could also be extended to the world level (Mexico, China, Japan, Malaysia, Pakistan, etc.) to evaluate the performance of the proposed hybrid time series modeling and forecasting technique. Moreover, only univariate time series models were used in this study, which should be extended by machine learning models such as deep learning and artificial neural networks. They can also be considered in the current hybrid time series forecasting framework. It can also be extended and applied to other approaches and datasets (for example, energy [42; 43; 44], air pollution [45; 46], solid waste [47], and academic performance [48]). **Author Contributions:** Conceptualization, N.C.-B., H.I., M.B. and J.L.L.-G.; methodology, software, and validation, H.I. ; formal analysis, H.I. and J.L.L.-G.; investigation, N.C.-B., H.I. and J.L.L.-G.; resources, N.C.-B., H.I., M.B., R.J.C.-T. and J.L.L.-G.; data curation, N.C.-B., H.I. and J.L.L.-G.; writing--original draft preparation, N.C.-B., H.I., M.B., R.J.C.-T., A.R.H.D.L.C. and J.L.L.-G.; writing--review and editing, N.C.-B., H.I., M.B., R.J.C.-T., A.R.H.D.L.C. and J.L.L.-G.; visualization, N.C.-B., H.I. and J.L.L.-G.; supervision, M.B. and J.L.L.-G.; project administration, H.I., M.B. and J.L.L.-G.; funding acquisition, M.B. and R.J.C.-T. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Institutional Review Board Statement:** Not applicable.