{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T16:29:29Z","timestamp":1778171369611,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T00:00:00Z","timestamp":1761868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Air pollution, outstanding particulate matter (PM2.5), poses severe risks to human health and the environment in densely populated urban areas. Accurate short-term forecasting of PM2.5 concentrations is therefore crucial for timely public health advisories and effective mitigation strategies. This work proposes a hybrid approach that combines machine learning models with STL decomposition to provide precise short-term PM2.5 predictions. Daily PM2.5 series from four major Pakistani cities\u2014Islamabad, Lahore, Karachi, and Peshawar\u2014are first pre-processed to handle missing values, outliers, and variance instability. The data are then decomposed via seasonal-trend decomposition using Loess (STL), which explicitly exploits the symmetric and recurrent structure of seasonal patterns. Each decomposed component (trend, seasonality, and remainder) is modeled independently using an ensemble of statistical and machine learning approaches. Forecasts are combined through a weighted aggregation scheme that balances bias\u2013variance trade-offs and preserves the distributional consistency. The final recombined forecasts provide one-day-ahead PM2.5 predictions with associated uncertainty measures. The model evaluation employs multiple statistical accuracy metrics, distributional diagnostics, and out-of-sample validation to assess its performance. The results demonstrate that the proposed framework consistently outperforms conventional benchmark models, yielding robust, interpretable, and probabilistically coherent forecasts. This study demonstrates how periodic and recurrent seasonal structure decomposition and probabilistic ensemble methods enhance the statistical modeling of environmental time series, offering actionable insights for urban air quality management.<\/jats:p>","DOI":"10.3390\/sym17111827","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:47:58Z","timestamp":1762177678000},"page":"1827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Hybrid STL-Based Ensemble Model for PM2.5 Forecasting in Pakistani Cities"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4993-9433","authenticated-orcid":false,"given":"Moiz","family":"Qureshi","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Sindh, Hyderabad 76080, Pakistan"},{"name":"Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7676-1020","authenticated-orcid":false,"given":"Atef F.","family":"Hashem","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8533-5410","authenticated-orcid":false,"given":"Hasnain","family":"Iftikhar","sequence":"additional","affiliation":[{"name":"Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan"},{"name":"Department of Statistics, University of Peshawar, Peshawar 25120, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1248-9910","authenticated-orcid":false,"given":"Paulo Canas","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Department of Statistics, Federal University of Bahia, Salvador 40170-110, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.5588\/ijtld.22.0249","article-title":"Outdoor air pollution and respiratory health","volume":"27","author":"Maio","year":"2023","journal-title":"Int. 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