{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T17:14:59Z","timestamp":1775841299523,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T00:00:00Z","timestamp":1748908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100018227","name":"National Research Foundation of Ukraine","doi-asserted-by":"publisher","award":["2023.03\/0197"],"award-info":[{"award-number":["2023.03\/0197"]}],"id":[{"id":"10.13039\/100018227","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Accurate forecasting of COVID-19 case numbers is critical for timely and effective public health interventions. However, epidemiological data\u2019s irregular and noisy nature often undermines the predictive performance. This study examines the influence of four smoothing techniques\u2014the rolling mean, the exponentially weighted moving average, a Kalman filter, and seasonal\u2013trend decomposition using Loess (STL)\u2014on the forecasting accuracy of four models: LSTM, the Temporal Fusion Transformer (TFT), XGBoost, and LightGBM. Weekly case data from Ukraine, Bulgaria, Slovenia, and Greece were used to assess the models\u2019 performance over short- (3-month) and medium-term (6-month) horizons. The results demonstrate that smoothing enhanced the models\u2019 stability, particularly for neural architectures, and the model selection emerged as the primary driver of predictive accuracy. The LSTM and TFT models, when paired with STL or the rolling mean, outperformed the others in their short-term forecasts, while XGBoost exhibited greater robustness over longer horizons in selected countries. An ANOVA confirmed the statistically significant influence of the model type on the MAPE (p = 0.008), whereas the smoothing method alone showed no significant effect. These findings offer practical guidance for designing context-specific forecasting pipelines adapted to epidemic dynamics and variations in data quality.<\/jats:p>","DOI":"10.3390\/computation13060136","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T06:21:51Z","timestamp":1748931711000},"page":"136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Smoothing Techniques for Improving COVID-19 Time Series Forecasting Across Countries"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6213-5531","authenticated-orcid":false,"given":"Uliana","family":"Zbezhkhovska","sequence":"first","affiliation":[{"name":"Scientific and Methodical Department for Quality Assurance of Educational Activities and Higher Education, Ivan Kozhedub Kharkiv National Air Force University, 61023  Kharkiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2623-3294","authenticated-orcid":false,"given":"Dmytro","family":"Chumachenko","sequence":"additional","affiliation":[{"name":"Mathematical Modelling and Artificial Intelligence Department, National Aerospace University \u201cKharkiv Aviation Institute\u201d, 61072 Kharkiv, Ukraine"},{"name":"Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"},{"name":"Ubiquitous Health Technology Lab, University of Waterloo, Waterloo, ON N2L 2G5, Canada"},{"name":"Balsillie School of International Affairs, Waterloo, ON N2L 6C2, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"key":"ref_1","unstructured":"World Health Organization (2024). COVID-19 Epidemiological Update\u2014Edition 177, World Health Organization. Available online: https:\/\/www.who.int\/publications\/m\/item\/covid-19-epidemiological-update-edition-177."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3708549","article-title":"Disease outbreak detection and forecasting: A review of methods and data sources","volume":"6","author":"Babanejaddehaki","year":"2025","journal-title":"ACM Trans. Comput. Healthc."},{"key":"ref_3","first-page":"100064","article-title":"Sustainable and intelligent time-series models for epidemic disease forecasting and analysis","volume":"3","author":"Chhabra","year":"2024","journal-title":"Sustain. Technol. Entrep."},{"key":"ref_4","first-page":"1","article-title":"STL decomposition and SARIMA model: The case for estimating value-at-risk of COVID-19 increment rate in DKI Jakarta","volume":"7","author":"Zahrani","year":"2021","journal-title":"Int. J. Inf. Commun. Technol. (IJoICT)"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jobb.2024.04.001","article-title":"Kalman filter based on a fractional discrete-time stochastic augmented COVID-19 model","volume":"6","author":"Ghani","year":"2024","journal-title":"J. Biosaf. Biosecur."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jiao, S., Wang, Y., Ye, X., Nagahara, L., and Sakurai, T. (2025). Spatio-temporal epidemic forecasting using mobility data with LSTM networks and attention mechanism. Sci. Rep., 15.","DOI":"10.1038\/s41598-025-94089-9"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jenko, J., Costa, J.P., Vladu\u0161i\u010d, D., Bav\u010dar, U., and \u010cabarkapa, R. (2024, January 8\u201311). Learning from the COVID-19 pandemic to improve critical infrastructure resilience using temporal fusion transformers. Proceedings of the Computer Science and Information Systems (FedCSIS), Belgrade, Serbia.","DOI":"10.15439\/2024F2959"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"71","DOI":"10.35784\/iapgos.3652","article-title":"Comparison of the effectiveness of time series analysis methods: SMA, WMA, EMA, EWMA, and Kalman filter for data analysis","volume":"13","author":"Lotysh","year":"2023","journal-title":"Inform. Autom. Pomiary Gospod. Ochr. \u015arodowiska"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kotu, V., and Deshpande, B. (2019). Time series forecasting. Data Science, Morgan Kaufmann. [2nd ed.].","DOI":"10.1016\/B978-0-12-814761-0.00012-5"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ouyang, Z., Ravier, P., and Jabloun, M. (2021). STL decomposition of time series can benefit forecasting done by statistical methods but not by machine learning ones. Eng. Proc., 5.","DOI":"10.3390\/engproc2021005042"},{"key":"ref_11","unstructured":"Khikmah, K.N., and Sofro, A. (2022). Autoregressive moving average and generalized autoregressive moving average in COVID-19 confirmed cases in Indonesia. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Abidi, F.A., and Radiy, Z.H. (2023, January 9\u201310). Using exponential smoothing methods to analysis COVID-19 time series. Proceedings of the 2nd International Conference on Engineering and Science to Achieve the Sustainable Development Goals, AIP Conference Proceedings, Tabriz, Iran.","DOI":"10.1063\/5.0200417"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"mzad058","DOI":"10.1093\/intqhc\/mzad058","article-title":"The optimal control chart selection for monitoring COVID-19 phases: A case study of daily deaths in the USA","volume":"35","author":"Waqas","year":"2023","journal-title":"Int. J. Qual. Health Care"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e81916","DOI":"10.7554\/eLife.81916","article-title":"Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations","volume":"12","author":"Sherratt","year":"2023","journal-title":"eLife"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hsu, C.-R., and Wang, H. (2025). EWMA control chart integrated with time series models for COVID-19 surveillance. Mathematics, 13.","DOI":"10.3390\/math13010115"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"104291","DOI":"10.1016\/j.rinp.2021.104291","article-title":"Volatility estimation for COVID-19 daily rates using Kalman filtering technique","volume":"26","author":"Mahmud","year":"2021","journal-title":"Results Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1007\/s10489-020-01948-1","article-title":"Kalman filter based short term prediction model for COVID-19 spread","volume":"51","author":"Singh","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"030067","DOI":"10.1063\/5.0081995","article-title":"Prediction of COVID-19 using Kalman filter algorithm","volume":"2418","author":"Rao","year":"2022","journal-title":"Proc. AIP Conf. Proc."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Nanda, S.K., Kumar, G., Bhatia, V., and Singh, A.K. (2023). Kalman-based compartmental estimation for COVID-19 pandemic using advanced epidemic model. Biomed. Signal Process. Control, 84.","DOI":"10.1016\/j.bspc.2023.104727"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s41549-022-00071-z","article-title":"COVID-19 and seasonal adjustment","volume":"18","author":"Abeln","year":"2022","journal-title":"J. Bus. Cycle Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e19115","DOI":"10.2196\/19115","article-title":"Prediction of the COVID-19 pandemic for the top 15 affected countries: Advanced autoregressive integrated moving average (ARIMA) model","volume":"6","author":"Singh","year":"2020","journal-title":"JMIR Public Health Surveill."},{"key":"ref_22","first-page":"1","article-title":"ARIMA model in predicting of COVID-19 epidemic for the Southern Africa region","volume":"17","author":"Claris","year":"2022","journal-title":"Afr. J. Infect. Dis."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Somyanonthanakul, R., Warin, K., Amasiri, W., Mairiang, K., Mingmalairak, C., Panichkitkosolkul, W., Silanun, K., Theeramunkong, T., Nitikraipot, S., and Suebnukarn, S. (2022). Forecasting COVID-19 cases using time series modeling and association rule mining. BMC Med. Res. Methodol., 22.","DOI":"10.1186\/s12874-022-01755-x"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jin, Y., Wang, R., Zhuang, X., Wang, K., Wang, H., Wang, C., and Wang, X. (2022). Prediction of COVID-19 data using an ARIMA-LSTM hybrid forecast model. Mathematics, 10.","DOI":"10.3390\/math10214001"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ahn, J.M., Kim, J., and Kim, K. (2023). Ensemble machine learning of gradient boosting (XGBoost, LightGBM, CatBoost) and attention-based CNN-LSTM for harmful algal blooms forecasting. Toxins, 15.","DOI":"10.2139\/ssrn.4434784"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13648","DOI":"10.1007\/s11356-022-23132-3","article-title":"A data-driven interpretable ensemble framework based on tree models for forecasting the occurrence of COVID-19 in the USA","volume":"30","author":"Zheng","year":"2023","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_27","first-page":"838","article-title":"COVID-19 prediction using LightGBM and LSTM","volume":"6","author":"Dharayani","year":"2022","journal-title":"J. Sains Komput. Inform."},{"key":"ref_28","first-page":"101364","article-title":"Advanced time complexity analysis for real-time COVID-19 prediction in Saudi Arabia using LightGBM and XGBoost","volume":"18","author":"Sadig","year":"2025","journal-title":"J. Radiat. Res. Appl. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104462","DOI":"10.1016\/j.rinp.2021.104462","article-title":"Time series prediction of COVID-19 transmission in America using LSTM and XGBoost algorithms","volume":"27","author":"Luo","year":"2021","journal-title":"Results Phys."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Chandra, R., Jain, A., and Singh Chauhan, D. (2022). Deep learning via LSTM models for COVID-19 infection forecasting in India. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0262708"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hu, B., Han, Y., Zhang, W., Zhang, Q., Gu, W., Bi, J., Chen, B., and Xiao, L. (2024). A prediction approach to COVID-19 time series with LSTM integrated attention mechanism and transfer learning. BMC Med. Res. Methodol., 24.","DOI":"10.1186\/s12874-024-02433-w"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1016\/j.ijforecast.2021.03.012","article-title":"Temporal Fusion Transformers for interpretable multi-horizon time series forecasting","volume":"37","author":"Lim","year":"2021","journal-title":"Int. J. Forecast."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.3390\/stats7040069","article-title":"Forecasting mortality trends: Advanced techniques and the impact of COVID-19","volume":"7","author":"Nalmpatian","year":"2024","journal-title":"Stats"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Elimam, R., Sutton-Charani, N., Perrey, S., and Montmain, J. (2022). Uncertain imputation for time-series forecasting: Application to COVID-19 daily mortality prediction. PLoS Digit. Health, 1.","DOI":"10.1371\/journal.pdig.0000115"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Sharif, O., Hasan, M.Z., and Rahman, A. (2022). Determining an effective short term COVID-19 prediction model in ASEAN countries. Sci. Rep., 12.","DOI":"10.1038\/s41598-022-08486-5"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"146","DOI":"10.59096\/osir.v17i3.270877","article-title":"Accuracy of COVID-19 prediction modeling techniques","volume":"17","author":"Thammawijaya","year":"2024","journal-title":"Outbreak Surveill. Investig. Response J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.18203\/2320-6012.ijrms20231344","article-title":"Comparison of exponential smoothing and ARIMA time series models for forecasting COVID-19 cases: A secondary data analysis","volume":"11","author":"Bahuguna","year":"2023","journal-title":"Int. J. Res. Med. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"100222","DOI":"10.1016\/j.iot.2020.100222","article-title":"Predicting the growth and trend of COVID-19 pandemic using machine learning and cloud computing","volume":"11","author":"Tuli","year":"2020","journal-title":"Internet Things"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Wong, L., and Goh, W.W.B. (2020). How to do quantile normalization correctly for gene expression data analyses. Sci. Rep., 10.","DOI":"10.1038\/s41598-020-72664-6"},{"key":"ref_40","first-page":"21","article-title":"Forecasting the COVID-19 increment rate in DKI Jakarta using non-robust STL decomposition and SARIMA model","volume":"7","author":"Satrisna","year":"2021","journal-title":"Int. J. Inf. Commun. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e2113561119","DOI":"10.1073\/pnas.2113561119","article-title":"Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States","volume":"119","author":"Cramer","year":"2022","journal-title":"Proc. Natl. Acad. Sci. USA"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/6\/136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:46:31Z","timestamp":1760031991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/6\/136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,3]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["computation13060136"],"URL":"https:\/\/doi.org\/10.3390\/computation13060136","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,3]]}}}