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Interpretable PM2.5 Forecasting for Urban Air Quality: A Comparative Study of Operational Time-Series Models
Moazzam Umer Gondal, Hamad ul Qudous, Asma Ahmad Farhan, Sultan Alamri
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Summary
This study evaluates the performance of three lightweight, interpretable time-series forecasting models (SARIMAX, Facebook Prophet, and NeuralProphet) for hourly PM2.5 prediction in Beijing. Using a leakage-aware workflow with exogenous meteorological and pollutant drivers, the authors compare two operational regimes: weekly walk-forward refitting and frozen-model forecasting with online residual correction. Results indicate that Facebook Prophet with residual correction offers a superior balance of predictive accuracy, computational efficiency, and interpretability compared to more complex deep learning alternatives.
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Facebook Prophet â outperformed â NeuralProphet
confidence 95% · Facebook Prophet achieved the strongest completed performance... while also requiring substantially less execution time than NeuralProphet.
SARIMAX â evaluatedin â Beijing
confidence 90% · This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China.
Online residual correction â improvedaccuracyof â Facebook Prophet
confidence 90% · In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX
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Abstract
Abstract:Accurate short-term air-quality forecasting is essential for public health protection and urban management, yet many recent forecasting frameworks rely on complex, data-intensive, and computationally demanding models. This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China. Using multi-year pollutant and meteorological time-series data, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, preprocessing, feature selection, and exogenous-driver modeling under the Perfect Prognosis setting. Three forecasting families were evaluated: SARIMAX, Facebook Prophet, and NeuralProphet. To assess practical deployment behavior, the models were tested under two adaptive regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. Results showed clear differences in both predictive accuracy and computational efficiency. Under walk-forward refitting, Facebook Prophet achieved the strongest completed performance, with an MAE of $37.61$ and an RMSE of $50.10$, while also requiring substantially less execution time than NeuralProphet. In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX, with corrected SARIMAX yielding the lowest overall error (MAE $32.50$; RMSE $46.85$). NeuralProphet remained less accurate and less stable across both regimes, and residual correction did not improve its forecasts. Notably, corrected Facebook Prophet reached nearly the same error as its walk-forward counterpart while reducing runtime from $15$ min $21.91$ sec to $46.60$ sec. These findings show that lightweight additive forecasting strategies can remain highly competitive for urban air-quality prediction, offering a practical balance between accuracy, interpretability, ...
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Interpretable PM2.5 Forecasting for Urban Air Quality: A Comparative Study of Operational Time-Series Models Moazzam Umer Gondal1, Hamad Ul Qudous1, Asma Ahmad Farhan1* Sultan Alamri 2 1 School of Computing, National University of Computer & Emerging Sciences (FAST), Lahore 54000, Pakistan 2 College of Computing and Informatics, Saudi Electronic University, Riyadh, 11673, Saudi Arabia * asma.ahmad@nu.edu.pk Abstract Accurate short-term air-quality forecasting is essential for public health protection and urban management, yet many recent forecasting frameworks rely on complex, data-intensive, and computationally demanding models. This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China. Using multi-year pollutant and meteorological time-series data, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, preprocessing, feature selection, and exogenous-driver modeling under the Perfect Prognosis setting. Three forecasting families were evaluated: SARIMAX, Facebook Prophet, and NeuralProphet. To assess practical deployment behavior, the models were tested under two adaptive regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. Results showed clear differences in both predictive accuracy and computational efficiency. Under walk-forward refitting, Facebook Prophet achieved the strongest completed performance, with an MAE of 37.6137.61 and an RMSE of 50.1050.10, while also requiring substantially less execution time than NeuralProphet. In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX, with corrected SARIMAX yielding the lowest overall error (MAE 32.5032.50; RMSE 46.8546.85). NeuralProphet remained less accurate and less stable across both regimes, and residual correction did not improve its forecasts. Notably, corrected Facebook Prophet reached nearly the same error as its walk-forward counterpart while reducing runtime from 1515 min 21.9121.91 sec to 46.6046.60 sec. These findings show that lightweight additive forecasting strategies can remain highly competitive for urban air-quality prediction, offering a practical balance between accuracy, interpretability, and computational efficiency for real-world deployment. Introduction Air pollution remains a major global environmental and public health challenge. Rapid urbanization, industrial emissions, and motorized transport continue to degrade air quality in major cities. Among pollutants, fine particulate matter (PM2.5) and coarse particles (PM10) are of particular concern because they penetrate deeply into the respiratory system, causing respiratory and cardiovascular diseases [33], while also reducing visibility and contributing to climate change. Cities such as Tehran and Beijing illustrate this global challenge, where frequent haze and high PM2.5 levels highlight the difficulty of real-time management and the need for accurate forecasting [9, 13]. Reliable forecasts are essential for public health and policy planning, as the WHO links over 4 million premature deaths in 2019 to air pollution [33]. Accurate short-term predictions of PM2.5 support timely warnings and interventions, yet forecasting in mega cities remains difficult due to microclimates and complex pollutant interactions [7]. Robust predictive frameworks also enable smart city functions such as adaptive traffic and health management [7, 29]. Research spans classical statistical methods to deep learning and hybrid decompositions. LSTM architectures have shown strong short-term performance, particularly when combined with meteorological drivers or hyperparameter tuning [6]. Decompositionâreconstruction pipelines (e.g., SSA/VMD plus LSTM or gradient boosting) improve fidelity by isolating multi-scale components, outperforming monolithic deep models [29, 35]. More recent hybrid deep learning frameworks, such as BiGRUâ1DCNN models for spatio-temporal PM2.5 forecasting, have further advanced prediction accuracy in urban settings [4]. Reviews emphasize the complementary value of such hybrids and the growing role of cloudâedge ecosystems [7, 35]. In parallel, federated learning preserves data locality across agencies while training global or personalized predictors. Surveys document the promise and challenges of federated learning, with applications including convolutionalârecurrent models [23], UAV-assisted prediction [5], and graph-based federated learning for non-Euclidean spatial structures [11]. While these approaches achieve high accuracy, they often introduce operational complexity and reduce transparency for policymakers. Forecasting PM2.5 in Beijing exemplifies several challenges: nonstationary signals with multi-scale seasonality, pollutantâpollutant coupling, and meteorological regimes that shift across months. Data gaps from sensor downtime and episodic haze require robust preprocessing and careful experimental design to prevent information leakage. Feature selection also remains crucial, as recent work highlights mutual-information filtering for spatio-temporal networks [30]. In this study, we revisit hourly particulate matter forecasting for Beijing through a transparent, operational lens. We compare three widely used time-series forecasting families that can incorporate exogenous driversâSARIMAX, Facebook Prophet, and NeuralProphetâand examine how their performance changes under two practical update strategies: frequent refitting versus lightweight online correction. Experiments are conducted in the Perfect Prognosis setting, enabling a focused assessment of forecasting and adaptation behavior. The proposed workflow integrates leakage-aware preprocessing and feature selection, and is evaluated using a rolling multi-week protocol to provide robust performance estimates over time. Our contributions are threefold: âą A transparent and leakage-aware forecasting workflow for hourly PM2.5 prediction under perfect prognosis, combining rigorous preprocessing with principled feature selection and exogenous-driver modeling. âą A systematic benchmark of SARIMAX, Facebook Prophet, and NeuralProphet under two deployment regimesâwalk-forward refitting and frozen forecasting with online residual correctionâusing a rolling evaluation design. âą Evidence that lightweight residual correction can substantially improve robustness to drift while preserving interpretability and reducing the operational cost associated with frequent retraining. Related work Research on air-quality forecasting has progressed from classical statistical baselines to machine learning (ML), deep learning (DL), and hybrid frameworks. Early models emphasized simplicity and interpretability but struggled with nonlinear, multivariate behavior. As sensing networks expanded and computation became cheaper, ML and DL methods advanced the state of the art by learning richer temporal and spatial dependencies. Hybrid pipelines further combined decomposition, feature selection, and model fusion to boost robustness and accuracy. Across this evolution, a key tension persists between predictive performance and the transparency required for policy use [19, 21, 7]. Classical statistical models such as ARIMA/SARIMA and multiple linear regression have long been applied to PM2.5, PM10, and AQI forecasting because they are data-efficient and interpretable [19]. Facebook Prophet revitalized additive regression as a modern baseline; studies reported that Prophet captured recurring seasonal patterns and often outperformed tuned SARIMA for short horizons [27, 1]. However, fixed parametric structures limit adaptability to regime shifts and high-dimensional inputs, as urban pollution is influenced by nonlinear meteorology and variable emissions [21]. While statistical approaches remain valuable for transparency and medium-range seasonality, their rigidity motivated the move toward ML and DL [19, 27, 1, 21]. ML methods offer flexibility for nonlinearities, heterogeneous covariates, and spatial transfer. Tree ensembles and margin-based learners are widely used: LightGBM leveraged high-dimensional spatio-temporal features for next-day PM2.5 across 35 Beijing stations [36], while evaluations across 23 Indian cities highlighted ensemble strength but also year-to-year drift [15]. End-to-end ML pipelines emphasize preprocessing, feature importance, and careful train/test design for Random Forest, SVM, and boosting methods [17]. Spatial generalization has been demonstrated via statewide PM2.5 surfaces with auxiliary covariates [18]. ML has also been adapted to atypical regimes such as mass rallies using temporally weighted multitask learning [8]. Recent work further explores robust ML rules for pollution trend detection, integrating PCA, clustering, and correspondence analysis to identify multimodal pollution regimes [22]. Comparative studies in Gulf-region meteorology showed that ML remains competitive with both DL and Prophet for one- to seven-day horizons [1]. Complementary findings show that optimized ML regressorsâparticularly SVR, LightGBM, and ensemble stacksâcan yield highly accurate forecasts when combined with Bayesian optimization and systematic preprocessing [26]. Surveys echo these findings: while DL often leads on accuracy, ML baselines retain reliability and integrate naturally with IoT-centric sensing for calibration and forecasting [21, 7, 17, 18]. DL now dominates for capturing long-range dependencies and complex multivariate dynamics. RNN variantsâespecially LSTM and Bi-LSTMâhave been applied at continental scale using attention mechanisms and heterogeneous data sources, improving event sensitivity and accuracy [32]. Hyperparameter tuning strongly affects performance, with optimized Bi-LSTM models outperforming untuned baselines [28]. Continuous-time formulations via Neural ODEs address irregular sampling and nonstationarity, yielding gains over conventional LSTM [10]. DL also accommodates atypical drivers: traffic and noise data improved PM10 forecasts in Skopje, with noise contributing more than traffic [14]. Hybrid DL pipelines combining decomposition and learning (e.g., Bi-LSTM with LightGBM) achieved further gains [34]. Despite progress, DL requires larger datasets and compute budgets and remains less transparent for operational agencies [32, 28, 10, 14, 34]. Hybrid and ensemble strategies integrate complementary strengths across decomposition, architecture fusion, and feature filtering. Decomposition-based hybrids (e.g., SSA or STL followed by specialized learners) improve stability by modeling trend/seasonal/noise components separately before recombination, achieving lower RMSE/MAE/SMAPE than vanilla deep baselines [34, 12]. Recent studies have continued to enhance hybrid architectures by integrating recurrent, convolutional, and boosting components. For example, BiGRUâ1DCNN frameworks have shown strong spatio-temporal learning performance across urban PM2.5 networks [4], while hybrid RNNâBiGRU models with advanced imputation methods improved robustness under missing data [3]. Similarly, WaveNet-inspired CNNâBiLSTMâXGBoost models achieved notable gains in multi-city forecasting accuracy [2]. Architectural fusion further combines global attention with local memory (TransformerâLSTM) and uses metaheuristics for hyperparameter tuning, delivering consistent gains across Chinese cities [20]. At the systems level, federated learning (FL) enables privacy-preserving collaboration under non-IID data and client drift, while IoTâAI stacks connect low-cost sensors to ML/DL modules for calibration and forecasting [16, 7]. Collectively, these hybrids enhance accuracy and robustness but also increase implementation complexity and operational overhead [34, 12, 4, 3, 2, 20, 31, 16, 7]. Despite this progress, two gaps persist. First, many studies continue to prioritize accuracy through increasingly complex pipelines, often at the expense of transparency and operational simplicityâqualities that are important for policy response and real-world deployment [7, 21]. Second, while decomposable time-series models have matured, systematic assessments of additive forecasting frameworks with exogenous drivers in air-pollution prediction remain comparatively limited. Models such as Facebook Prophet and NeuralProphet explicitly encode trend and seasonality and can incorporate external regressors, offering lightweight and interpretable alternatives to heavy deep-learning pipelines [27, 1]. Moreover, practical deployment raises an additional challenge that is less frequently isolated in prior comparisons: temporal drift and the cost of keeping models up to date. This study addresses these gaps by benchmarking SARIMAX, Facebook Prophet, and NeuralProphet for hourly PM2.5 forecasting and by comparing two operational update strategiesâwalk-forward refitting and lightweight online residual correctionâto quantify the trade-off between adaptivity and retraining overhead. A condensed summary of representative studies discussed is provided in Table LABEL:tab:lr. Table 1: Condensed summary of representative literature. # Task/Target Data/Region Method and key highlights [7] IoT AQM + AI (review) PRISMA 2016â2024 Systematic review; taxonomy (imputation, calibration, anomalies, AQI, short-term forecasting); stresses data quality, scalability, and deployment gaps. [4] PM2.5 forecasting (spatio-temporal hybrid) Delhi, India (2018â2023) BiGRUâ1DCNN hybrid integrates recurrent and convolutional layers for spatio-temporal learning across 28 CPCB stations; achieves low RMSE/MAE and strong seasonal trend capture. [19] AQI forecast; statistical vs N Beijing, China ARIMA + ANN; linear vs nonlinear contrast; hybridization aids robustness; seasonality handling highlighted. [21] Review of AI techniques for air-pollution forecasting Global survey (2000â2020) Comprehensive review of AI/ML methods including SVM, ensembles, and DL; highlights evolution from statistical to hybrid models. [27] Univariate short-horizon forecast (pollutants/AQI) City station series SARIMA vs Prophet; additive seasonality and log-transform improve short-horizon accuracy; interpretable baseline for ML/DL. [1] PM2.5/PM10 comparison UAE monitoring sites DT/RF/SVR vs CNN/LSTM vs Prophet; ML competitive across 1â7 day horizons; notes climate-specific transfer. [36] Next-day PM2.5/AQI (station-level) 35 Beijing stations LightGBM with rich spatio-temporal covariates; systematic feature exploration; strong non-DL baseline with interpretable importances. [15] AQI classification/regression 23 Indian cities, 6 years (CPCB) Multi-model ML benchmark (NB/SVM/XGBoost); correlation-based feature selection; evidences data drift and generalization issues. [17] AQI events at 1/8/24 h Event-focused datasets End-to-end ML pipeline (RF/AdaBoost/SVM/ANN/stacking); preprocessing and horizon design matter; ensembles often strongest. [18] Spatially continuous PM2.5 New York State, USA Statewide predictive mapping from monitors plus auxiliary covariates; improved spatial generalization for exposure assessment. [8] Multi-pollutant during mass rallies Event-driven series Temporally weighted multitask learner; reweights in time, shares across pollutants, and handles distribution shift. [22] Pollution trend detection (robust ML) Southern China, Hong Kong, Macau (multi-year) EstiMax and SMA algorithms integrate PCA, clustering, EM, and correspondence analysis to identify multimodal pollution regimes and seasonal patterns. [26] ML forecasting (optimization + ensembles) Hourly sensor data (1 year) Comparative study of ten ML regressors; Bayesian optimization and stacking markedly improve SVR, LightGBM, and boosting models. [32] Daily PM2.5 estimation CONUS (USA) Bi-LSTM + Attention; fuses in-situ, satellite, and wildfire smoke data; better extreme-event capture and high-resolution national surfaces. [28] PM2.5 estimation Multi-feature stations Bi-LSTM with Osprey hyperparameter optimization; tuned deep models outperform untuned baselines. [10] Short-horizon PM2.5 (1â8 h) Irregular sampling Neural-ODE variants; continuous-time dynamics; gains versus LSTM and robustness under irregular intervals. [14] PM10 with exogenous signals Skopje (urban) LSTM-family with traffic and noise; noise aids prediction; traffic not always dominant. [34] Hourly AQI, 1-step/multi-step Beijing, China SSA â Bi-LSTM per component â LightGBM stack; decomposition stabilizes and stacking boosts generalization. [12] PM2.5 via component tailoring Five Chinese cities STL plus component-specific learners; improves MSE/MAE/MAPE/R2R^2 and robustness to nonstationarity. [3] PM2.5 forecasting with missing-data handling Lucknow, India (2020â2023) nRI RNNâBiGRU hybrid combines novel random imputation with bidirectional recurrent modeling; improves robustness under sensor data gaps. [2] Global urban PM2.5 forecasting (hybrid deep ensemble) Multi-city (US embassies, 2017â2024) 1DCNNâBiLSTMâXGBoost hybrid achieves high accuracy via residual correction across diverse climatic and pollution conditions. [20] PM2.5 model fusion Central/Western China Transformer â LSTM with PSO tuning; combines global attention and local memory for consistent gains. [16] AQI under privacy constraints FL/edge settings Multi-Model FL survey; discusses non-IID data, client drift, communication costs, and open challenges. [31] PM2.5 with input curation Multi-scenario evaluation MI + AID feature filtering â Bayes-optimized STCN; reduces redundancy and stabilizes training. The remainder of this paper is organized as follows. Methodology describes the dataset, preprocessing steps, forecasting models, adaptive regimes, and evaluation protocol, while Implementation provides the technical details required to reproduce the experimental workflow. Results presents the comparative forecasting performance under both deployment regimes. Discussion and Future Work interprets the main findings and outlines potential research directions. Limitations highlights the principal constraints of the current study, and Conclusion summarizes the overall contributions and practical implications. Methodology We formulate hourly PM2.5 forecasting for Beijing as a multistep time-series prediction task with exogenous drivers. Given observations up to time t, the objective is to forecast the next 7 days (168 hours). We conduct experiments under the Perfect Prognosis (P) assumption, where future values of the exogenous regressors over the forecast horizon are treated as known, allowing us to focus on comparing forecasting strategies rather than regressor prediction. The data are kept in chronological order and divided into 90% training and 10% test segments. Performance is evaluated on the test period using a rolling weekly protocol (horizon = 7 days, step = 7 days), producing multiple weekly forecast windows whose errors are aggregated. Within this framework, we benchmark SARIMAX, Facebook Prophet, and NeuralProphet and examine two practical deployment regimes: weekly walk-forward refitting and a frozen base model with lightweight online residual (bias) correction to handle drift with minimal retraining overhead. The workflow is shown in Fig 1. Fig 1: Framework of the proposed forecasting workflow. The workflow shows data preparation, chronological trainâtest partitioning, the forecasting setup, benchmarking of three forecasting model families, comparison of two operational regimes, and performance evaluation for air quality forecasting. Data preprocessing An hourly time series for Beijing was compiled spanning December 2020 to June 2025. Pollutant concentrations (PM2.5, PM10, CO, NO, NO2, SO2, O3, NH3) were retrieved from the OpenWeather Air Pollution API [25], while meteorological variables (temperature and dew point) were obtained from Open-Meteo [24]. Both services provide model-based gridded estimates at user-specified coordinates rather than measurements from identifiable monitoring stations; therefore, detailed information about the number, placement, and specifications of contributing sensors is not disclosed by the providers. All data streams were temporally aligned and sorted by timestamp, and a continuous hourly index was enforced to ensure a regular sampling grid. After alignment, the dataset contained no missing timestamps and no missing values; hence, no imputation was required. To reduce the influence of extreme values while preserving sample size, outliers were handled via winsorization using training-set percentile bounds. For each variable, observations below the lower percentile bound and above the upper percentile bound were clipped to those respective bounds, producing a bounded series without discarding records; in walk-forward evaluation, these bounds were recomputed from the expanding training window only. For leakage-safe normalization, exogenous regressors were standardized using statistics computed only from the training segment and the same transformation was applied to the test segment. In the walk-forward evaluation, standardization was applied using statistics computed from the training window only. The target variable (PM2.5) was retained in its original units to maintain interpretability. All variables were kept at hourly resolution and passed to the subsequent feature selection stage. Feature selection To identify informative yet non-redundant predictors for PM2.5 forecasting, we applied three complementary filter-based criteria: Pearson correlation, mutual information (MI), and minimum redundancyâmaximum relevance (mRMR). Pearson correlation between variables X and Y is defined as ÏX,Y=Covâ(X,Y)ÏXâÏY _X,Y= Cov(X,Y) _X _Y (1) where Covâ(X,Y)Cov(X,Y) denotes covariance and ÏX _X, ÏY _Y are the corresponding standard deviations, capturing linear dependence. Mutual information quantifies potentially nonlinear associations via Iâ(X;Y)=âxâypâ(x,y)âlogâĄpâ(x,y)pâ(x)âpâ(y)I(X;Y)= _x _yp(x,y)\, p(x,y)p(x)p(y) (2) where pâ(x,y)p(x,y) is the joint probability mass or density function and pâ(x)p(x), pâ(y)p(y) are the marginals. Finally, mRMR selects features that are both highly relevant to the target and minimally redundant with already selected predictors: mRMR=maxfâFâSâĄ[Iâ(f;y)â1|S|ââsâSIâ(f;s)]mRMR= _fâ F S [I(f;y)- 1|S| _sâ SI(f;s) ] (3) where F denotes the candidate feature pool, S the currently selected subset, y the target (PM2.5), and Iâ(â ;â )I(·;·) represents mutual information. To prevent information leakage, all feature ranking and selection steps were performed using the training segment only; the resulting feature set was then fixed and used unchanged for validation and testing. This procedure yields a compact predictor set that remains strongly associated with PM2.5 while avoiding redundant covariates. Forecasting models We benchmark three representative forecasting model families for hourly PM2.5 prediction with exogenous drivers: a classical linear time-series model with external inputs (SARIMAX), a decomposable additive model (Facebook Prophet), and a neural extension of the same decomposable paradigm (NeuralProphet). Each model is used to produce multi-step (168-hour) forecasts under the perfect prognosis setting, i.e., exogenous regressors over the forecast horizon are assumed available. SARIMAX Seasonal autoregressive integrated moving-average with exogenous regressors (SARIMAX) models the target as a linear function of its past values, seasonal dynamics, and contemporaneous external covariates. A generic SARIMAX form can be written as yt=c+Ï1âytâ1+Ξ1âΔtâ1+Ί1âytâs+Î1âΔtâs+ÎČâXt+Δty_t=c+ _1y_t-1+ _1 _t-1+ _1y_t-s+ _1 _t-s+ÎČ X_t+ _t (4) where yty_t is the pollutant concentration at time t, Δt _t white noise, XtX_t exogenous regressors, Ï1 _1, Ί1 _1 autoregressive terms, Ξ1 _1, Î1 _1 moving-average terms, and s the seasonal period. (Ï1,Ξ1)( _1, _1) and (Ί1,Î1)( _1, _1) capture non-seasonal and seasonal autoregressive and moving-average dynamics, and XtX_t introduces external pollutant predictors. SARIMAX serves as a transparent statistical baseline that captures linear autocorrelation and seasonality while explicitly quantifying the contribution of external drivers through ÎČ. Facebook Prophet (FBP) Prophet is a decomposable additive model that represents the series as the sum of interpretable components, typically including a piecewise trend, multiple seasonalities, and the effect of external regressors. In its standard form, yâ(t)=gâ(t)+sâ(t)+hâ(t)+Ï”ty(t)=g(t)+s(t)+h(t)+ _t (5) where gâ(t)g(t) denotes a trend function (e.g., piecewise linear with changepoints), sâ(t)s(t) captures seasonal structure using Fourier series terms, hâ(t)h(t) represents the contribution of exogenous regressors (additively in our setting), and Ï”t _t is noise. The decomposition is well-suited for pollution time series in which long-term drift and recurring temporal patterns coexist with covariate-driven variability. NeuralProphet (NP) NeuralProphet extends the Prophet formulation by learning decomposable components using neural network parameterizations and by optionally incorporating autoregressive structure to better capture short-term dynamics. A general representation is yâ(t)=Tâ(t)+Sâ(t)+Eâ(t)+Aâ(t)+Fâ(t)+Lâ(t)y(t)=T(t)+S(t)+E(t)+A(t)+F(t)+L(t) (6) where Tâ(t)T(t) and Sâ(t)S(t) denote trend and seasonal components, Eâ(t)E(t) represents event effects when used, and Aâ(t)A(t) captures autoregressive dependence on lagged targets. Fâ(t)F(t) and Lâ(t)L(t) correspond to contributions from future-known and lagged regressors, respectively. This hybrid design preserves interpretability through explicit components while enabling more flexible nonlinear fitting of temporal and covariate effects. Adaptive forecasting regimes To study robustness to temporal drift while maintaining low operational complexity, we evaluate each forecasting model under two adaptive deployment regimes. The full time series is kept in chronological order and partitioned into a 90% training segment and a 10% test segment. Forecasts are generated over the test period in weekly windows (horizon = 168 hours, step = 168 hours). Under the perfect prognosis setting, the true exogenous regressors for each forecast window are provided to the models. The regimes differ only in how the forecasting model is updated, or not updated, as new observations become available. Regime 1: Weekly walk-forward refit In the walk-forward regime, the forecasting model is re-estimated at the start of every test week using all data observed up to that point. Specifically, let trainD_train denote the initial training set and let 1:wâ1D_1:w-1 denote the sequence of observed test weeks prior to week w. At the beginning of week w, the model is refit on (w)=trainâȘ1:wâ1D^(w)=D_train _1:w-1 (7) and then used to generate a 168-hour forecast for week w. This regime serves as a strong adaptive baseline that continuously incorporates the most recent dynamics, at the cost of repeated retraining. Regime 2: Frozen base model with online residual correction In the proposed low-cost regime, a base forecaster is trained once on the initial training set and then kept frozen during testing. Adaptation is achieved through a lightweight online correction applied to the model outputs using recently observed forecast errors. Let y^tbase y^base_t be the frozen model prediction and define the one-step residual as et=ytây^tbasee_t=y_t- y^base_t (8) At the end of each test week, the residuals from that week are summarized into a scalar bias (offset) estimate that is carried forward to correct the next weekâs forecast. Denote by eÂŻw e_w the mean residual over week w, computed as eÂŻw=1|w|ââtâwet e_w= 1|w| _tâ we_t (9) where |w|=168|w|=168 for a full week. For initialization, we set the bias state for the first forecast window to b1=0b_1=0 (no correction) and compute eÂŻ1 e_1 once observations for week 1 become available. Subsequent bias states are then updated recursively using an exponentially weighted moving average (EWMA): bw=αâeÂŻwâ1+(1âα)âbwâ1b_w=α\, e_w-1+(1-α)\,b_w-1 (10) where αâ(0,1)αâ(0,1) controls adaptivity (larger α reacts more strongly to the latest week). Alternatively, a Kalman-filter style update can be used to obtain bwb_w as a recursively estimated latent bias term (details provided in the implementation section). The corrected forecast for week w is formed as y^tfinal=y^tbase+bw,tâweek âw y^final_t= y^base_t+b_w, t w (11) This strategy preserves the stability and low overhead of a frozen forecasting model while enabling rapid adjustment to level shifts and gradual drift through an online bias term, without full retraining at each step. Rolling evaluation protocol Evaluation is performed on the held-out 10% test segment using a rolling weekly procedure designed to emulate repeated 7-day deployments. Specifically, the test interval is partitioned into consecutive, non-overlapping windows of length 168 hours (7 days). For each window w, a model produces a multi-step forecast y^ttâw\ y_t\_tâ w using information available up to the forecast origin, with a step size of 168 hours between successive origins (i.e., horizon = step = 168). This yields a sequence of weekly forecasts spanning the entire test period, enabling robust performance estimates over multiple forecast instances rather than a single terminal week. Forecast accuracy is quantified using mean absolute error (MAE) and root mean squared error (RMSE) computed over the predicted hours within each weekly window: MAE =1Nââi=1N|yiây^i| = 1N _i=1^N|y_i- y_i| (12) RMSE =1Nââi=1N(yiây^i)2 = 1N _i=1^N(y_i- y_i)^2 (13) where yiy_i and y^i y_i denote observed and predicted PM2.5 values and N is the number of evaluated hours. Window-level errors are then aggregated across all test windows and summarized using their mean values, providing an overall estimate of forecasting performance over the test period. Metrics such as MAPE and SMAPE are not used because they can be unstable when concentrations approach zero. Visual comparisons between predicted and observed trajectories over representative weeks are also provided to complement the quantitative summaries. Statistical analysis All analyses were conducted on chronologically ordered hourly time-series data under a forecasting design rather than a hypothesis-testing experimental design. Preprocessing included temporal alignment, leakage-safe standardization of exogenous regressors using training-set statistics only, and winsorization-based treatment of extreme values; no missing values were present after alignment, so no imputation was required. Feature selection was performed using Pearson correlation, mutual information, and mRMR on the training segment only to avoid information leakage. Model performance was evaluated on the held-out test segment using a rolling weekly protocol, and forecast accuracy was summarized across windows using mean MAE and mean RMSE. No formal null-hypothesis significance testing or multiple-comparison correction was applied, as model comparison was based on repeated out-of-sample forecasting errors under a fixed chronological evaluation design. Data processing scripts, forecasting code, and supporting analysis materials required to reproduce the reported results are available in the project GitHub repository. Implementation The experimental workflow was implemented in Python 3.12 using open-source scientific computing and time-series libraries in a Google Colab environment with access to an NVIDIA T4 GPU (16 GB GDDR6 VRAM). Data handling and preprocessing were carried out using pandas, numpy, and scikit-learn, while feature selection employed pymrmr. Forecasting experiments were conducted using statsmodels, prophet, and neuralprophet. NeuralProphet training leveraged GPU acceleration through its PyTorch-based backend, and visualizations were produced using matplotlib. Overall, the implementation covered the complete pipeline from preprocessing and feature selection to model fitting, adaptive updating, and rolling-window evaluation. Data assembly and preprocessing Hourly pollutant and meteorological series spanning December 2020 to June 2025 were assembled and aligned on a continuous hourly timestamp index. The merged dataset contained no missing timestamps or missing values after alignment. The series was then partitioned chronologically into 90% training and 10% test segments. To limit the effect of extreme anomalies while preserving all observations, winsorization was applied using training-set percentile bounds at the 1st and 99th percentiles. In the walk-forward regime, these bounds were recomputed from the expanding training window available at each forecast origin, ensuring that no future data were used during preprocessing. Exogenous regressors were standardized using training-set statistics only, while PM2.5 was retained in its original scale. Under the Perfect Prognosis setting, future regressor values for each 168-hour forecast window were taken from the held-out test segment and transformed using the same fitted scaler before being passed to the models. Feature selection Feature selection was implemented using correlation analysis, mutual information (MI), and minimum redundancyâmaximum relevance (mRMR), consistent with the methodology. Correlation analysis (Fig 2) was used to inspect linear associations among candidate variables, while MI (Fig 3) was used to assess nonlinear relevance to PM2.5. mRMR was then applied to retain informative predictors while reducing redundancy among highly correlated variables. Fig 2: Correlation heatmap of candidate variables. The heatmap shows strong linear associations between PM2.5 and several gaseous precursors, as well as between PM2.5 and PM10. Fig 3: Mutual information scores for candidate predictors with respect to PM2.5. The figure highlights the strongest nonlinear dependencies used to guide feature selection. The analysis showed that gaseous precursors were consistently among the most relevant predictors, whereas meteorological variables exhibited comparatively weaker influence. PM10 emerged as the strongest companion predictor to PM2.5, indicating clear cross-dependence between particulate fractions. However, PM10 was not included in the final exogenous set because of its strong redundancy with the target and to preserve a deployment-oriented feature subset based on precursor variables. Based on these considerations, the final exogenous feature set used for PM2.5 forecasting was NO, NO2, CO, SO2. Model configuration SARIMAX SARIMAX was configured with order (1,1,1)(1,1,1) and seasonal order (1,1,1,24)(1,1,1,24) to capture short-term dependence together with hourly seasonal structure. For PM2.5 forecasting, the exogenous regressor set comprised NO, NO2, CO, SO2. Multi-step forecasts over each 168-hour window were generated directly using the known future values of these regressors under the perfect prognosis setting. Facebook Prophet Facebook Prophet was configured with its default additive trend formulation and default changepoint handling. Daily, weekly, and yearly seasonalities were enabled, and the selected exogenous predictors were incorporated as additional regressors. For each forecast origin, the model generated predictions over the subsequent 168 hourly time steps using the corresponding future regressor values. NeuralProphet NeuralProphet was configured with daily, weekly, and yearly seasonalities enabled. To support direct multi-step forecasting, the model used n_lags=168 and n_forecasts=168, allowing one full week of past observations to inform one full week ahead. Training was performed for 30 epochs with a batch size of 128 and a learning rate of 0.001, without early stopping. The same selected exogenous variables were supplied as future regressors under the perfect prognosis setting. Adaptive regime implementation In the walk-forward setting, each model was re-estimated at the start of every weekly test window using the initial training data together with all observations revealed from prior test weeks. A new 168-hour forecast was then generated for the next window. In the frozen-model setting, each forecaster was fitted once on the initial 90% training segment and kept unchanged thereafter. Adaptation was introduced through an exponentially weighted moving average (EWMA) residual correction with fixed smoothing factor α=0.3α=0.3. The initial bias term was set to zero for the first forecast week. After each weekly window became fully observable, its mean residual was used to update the bias term, which was then added to the base predictions for the following week. Both regimes were executed over consecutive non-overlapping weekly windows, and their outputs were compared using the same MAE/RMSE aggregation procedure described in the methodology. Results Results are reported for hourly PM2.5 forecasting under the two deployment regimes introduced in the methodology: weekly walk-forward refitting and frozen forecasting with online residual correction. For each regime, we summarize overall mean absolute error (MAE), overall root mean squared error (RMSE), and observed end-to-end execution time. In addition to overall metrics, week-level MAE patterns are examined to characterize the stability of each model across the 23 rolling forecast windows. Regime 1: Weekly walk-forward refitting Quantitative results for the weekly walk-forward refitting regime are summarized in Table 2. Among the models that completed the rolling evaluation, Facebook Prophet (FBP) achieved the strongest overall performance, with an MAE of 37.61 and an RMSE of 50.10. NeuralProphet (NP) produced substantially larger forecast errors, with an MAE of 140.55 and an RMSE of 228.87. FBP was also markedly more efficient, completing in 15 min 21.91 s compared with 88 min 35.19 s for NP. SARIMAX could not be sustained through the full walk-forward experiment because repeated weekly refitting caused memory usage to increase substantially in the available computing environment. However, results were obtained up to week 21, at which point the cumulative MAE was 39.61 and the cumulative RMSE was 56.32, with execution time already exceeding 100 minutes. These partial results suggest that SARIMAX remained competitive in predictive terms, but at a considerably higher computational cost than FBP. Table 2: Overall performance under weekly walk-forward refitting. For SARIMAX, values are cumulative results obtained up to week 21 because the full run could not be completed in the available environment. Model MAE RMSE Execution time Remark NeuralProphet 140.55 228.87 88 min 35.19 s Full 23-week evaluation completed Facebook Prophet 37.61 50.10 15 min 21.91 s Full 23-week evaluation completed SARIMAX 39.61 56.32 >>100 min Cumulative results available only up to week 21 because of memory-related termination Week-level behavior further highlights the contrast between models. For NP, performance varied widely across the rolling windows, with the best weekly MAE observed in week 23 of 23 (28.46) and the worst in week 2 of 23 (424.28), indicating substantial instability under walk-forward retraining. FBP was much more stable, ranging from a best weekly MAE of 18.58 in week 1 to a worst weekly MAE of 69.78 in week 18. For SARIMAX, among the weeks that were successfully evaluated, the best weekly MAE was 8.77 in week 5 and the worst was 92.84 in week 17. Representative weekly forecasts for NeuralProphet, Facebook Prophet, and SARIMAX under weekly walk-forward refitting are shown in Fig 4, Fig 5, and Fig 6, respectively. Fig 4: Representative weekly forecasts for NeuralProphet under weekly walk-forward refitting. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. Fig 5: Representative weekly forecasts for Facebook Prophet under weekly walk-forward refitting. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. Fig 6: Representative weekly forecasts for SARIMAX under weekly walk-forward refitting. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. Overall, these results indicate that, under weekly walk-forward refitting, FBP offered the best practical balance between predictive accuracy, runtime, and stability. Although SARIMAX showed competitive partial forecasting accuracy, its computational burden made sustained repeated refitting difficult in the present setting. NP was both slower and markedly less stable, with very large errors in difficult weeks. Regime 2: Frozen forecasting with online residual correction Table 3 reports the results for the frozen-model regime, including both the original base forecasts and the forecasts after online residual correction. In this setting, the impact of correction differed substantially across models. For NP, residual correction did not improve performance. The corrected forecasts were worse than the base forecasts, with MAE increasing from 145.75 to 162.14 and RMSE increasing from 239.95 to 247.21. By contrast, FBP benefited from correction, with MAE decreasing from 45.61 to 37.67 and RMSE decreasing from 60.39 to 50.08. SARIMAX showed the largest gain, with MAE decreasing from 47.14 to 32.50 and RMSE decreasing from 65.45 to 46.85, yielding the lowest corrected error among all models in this regime. Table 3: Overall performance under frozen forecasting with online residual correction. Base metrics refer to the frozen model without correction, and corrected metrics refer to the same model after online residual correction. Execution time denotes the observed end-to-end runtime for the full regime. Model Base MAE Corrected MAE Base RMSE Corrected RMSE Execution time NeuralProphet 145.75 162.14 239.95 247.21 7 min 30.68 s Facebook Prophet 45.61 37.67 60.39 50.08 0 min 46.60 s SARIMAX 47.14 32.50 65.45 46.85 12 min 58.94 s The magnitude of the correction effect is also evident from the MAE changes. For FBP, correction reduced MAE by 7.93, whereas for SARIMAX the reduction was 14.64. In contrast, NP exhibited a deterioration of -16.39 in MAE after correction. A similar pattern was observed in RMSE, which decreased by 10.31 for FBP and 18.60 for SARIMAX, but increased by 7.26 for NP. Week-level results support the same interpretation. For NP, the corrected forecasts still exhibited large variability, ranging from a best corrected weekly MAE of 32.16 in week 22 of 23 to a worst corrected weekly MAE of 506.52 in week 2 of 23. FBP remained comparatively stable, with a best weekly MAE of 18.58 in week 1 and a worst weekly MAE of 69.60 in week 18. SARIMAX again showed strong corrected performance, ranging from a best weekly MAE of 9.96 in week 5 to a worst weekly MAE of 64.36 in week 18. Representative weekly forecasts for NeuralProphet, Facebook Prophet, and SARIMAX under frozen forecasting with online residual correction are shown in Fig 7, Fig 8, and Fig 9, respectively. Fig 7: Representative weekly forecasts for NeuralProphet under frozen forecasting with online residual correction. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. Fig 8: Representative weekly forecasts for Facebook Prophet under frozen forecasting with online residual correction. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. Fig 9: Representative weekly forecasts for SARIMAX under frozen forecasting with online residual correction. The plot shows the best weekly forecast in the upper panel and the worst weekly forecast in the lower panel across the rolling evaluation. The x-axis denotes hour of week (0â168), and the y-axis denotes PM2.5 concentration. These findings show that online residual correction was not universally beneficial, but it was highly effective for FBP and especially for SARIMAX. Notably, corrected FBP reached nearly the same overall error as walk-forward FBP (MAE 37.67 versus 37.61; RMSE 50.08 versus 50.10) while reducing execution time from 15 min 21.91 s to only 46.60 s. Comparison across deployment regimes A comparison across the two deployment regimes reveals three main findings. First, under weekly walk-forward refitting, FBP clearly outperformed NP and maintained much lower execution time. Second, in the frozen-model setting, lightweight residual correction allowed FBP to recover nearly the same accuracy as its walk-forward counterpart at a fraction of the computational cost, making it especially attractive for operational deployment. Third, the strongest absolute performance observed in the present experiments was obtained by corrected SARIMAX in the frozen regime, which achieved the lowest overall MAE and RMSE among the completed runs. Taken together, the results suggest that model choice depends not only on predictive accuracy but also on deployment constraints. FBP delivered the most favorable accuracyâefficiency trade-off across both regimes, while SARIMAX became highly competitive only when repeated full refitting was avoided. By contrast, NP remained both less accurate and less stable in the present experimental setting, and online residual correction did not mitigate this weakness. Discussion and Future Work The results highlight that competitive air-quality forecasting does not necessarily require highly complex, data-hungry, or computationally intensive pipelines. In contrast to many recent forecasting frameworks that rely on deep hybrid architectures and large-scale retraining, the present study shows that lightweight additive models can provide strong predictive performance with substantially lower operational cost. In particular, Facebook Prophet maintained a favorable balance between accuracy, stability, and execution time across both deployment regimes, while residual-corrected SARIMAX further demonstrated that simple adaptive mechanisms can recover strong performance without repeated full-model retraining. These findings are especially relevant for practical forecasting settings, where interpretability, computational efficiency, and ease of deployment are as important as raw predictive accuracy. Future work will extend this framework toward more adaptive and transferable forecasting strategies. One promising direction is the integration of lightweight hybrid techniques that combine interpretable additive models with targeted correction or decomposition modules to improve robustness under changing pollution regimes. Another important direction is the exploration of federated learning schemes, enabling privacy-preserving model sharing across distributed monitoring networks while improving generalization across diverse urban environments. Extending lightweight adaptation strategies to heterogeneous datasets, cities, and sensing conditions will be important for assessing the broader applicability of the proposed approach. Limitations Several limitations should be acknowledged. First, the dataset was obtained through public API services that provide aggregated pollutant and meteorological estimates, and therefore detailed information about the underlying monitoring stations, sensor composition, calibration procedures, and exact data-generation pipeline was not available. As a result, the analysis was conducted on the provided hourly series without direct control over the original sensing infrastructure. Second, the reported results reflect Beijingâs emission profile, seasonal pollution cycles, and local meteorological dynamics and may not transfer directly to cities with different source compositions, atmospheric conditions, or urban structures. Finally, although Prophet-based approaches are generally robust to recurring temporal patterns and gradual drift, substantial discontinuities or abrupt regime shifts could still affect their stability and forecasting reliability. Conclusion This study addressed the problem of short-term urban air-quality forecasting by examining whether lightweight and interpretable forecasting frameworks can remain competitive against more complex and computationally demanding approaches. Focusing on hourly PM2.5 prediction for Beijing, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, robust preprocessing, feature selection, and exogenous-driver modeling within the perfect prognosis setting. Three forecasting familiesâSARIMAX, Facebook Prophet, and NeuralProphetâwere evaluated under two practical deployment regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. The findings show that lightweight additive modeling remains a strong and practical alternative for operational air-quality forecasting. Facebook Prophet achieved the most favorable balance between predictive accuracy, stability, and computational efficiency across both regimes, while residual-corrected SARIMAX demonstrated that simple adaptive correction can substantially improve performance without repeated full retraining. Overall, the study shows that transparent and computationally efficient forecasting strategies can provide robust air-quality predictions, making them well suited for real-world deployment where interpretability, low overhead, and ease of maintenance are important considerations. Data Availability All data and code required to reproduce the findings of this study are publicly available in the project GitHub repository. Acknowledgments The authors have no acknowledgments to declare. References [1] W. Abuouelezz, N. Ali, Z. Aung, A. Altunaiji, S. B. Shah, and D. Gliddon (2025) Exploring PM2.5 and PM10 ML forecasting models: a comparative study in the UAE.. Scientific Reports 15, p. 9797. 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