Time-series visibility graph and histogram-based gradient boosting regressor (TSVG-HGBR) for robust multi-horizon urban carbon monoxide forecasting

Urban carbon monoxide (CO) concentrations fluctuate with traffic patterns, meteorological conditions, and industrial activities, yet existing statistical and machine learning models struggle to maintain predictive accuracy across extended forecasting horizons. This study introduces TSVG-HGBR, a hybrid framework that encodes Time-Series Visibility Graph topology features and a continuous data quality score into a Histogram-based Gradient Boosting Regressor to improve prediction robustness under degraded sensor conditions and across extended forecasting horizons. Using six years of half-hourly CO sensor data (2019–2024) from Semarang, Indonesia, the dataset (105,216 observations; 24.5% missing in raw) was partitioned into 80% training and 20% test sets using a strict chronological split. The proposed method was evaluated against ARIMA(2,1,1), SARIMA(log)(2,1,0)(1,1,0)[24], and standalone HGBR across two data quality scenarios (KNN-imputed and raw sensor data with missing values) and two forecasting horizons (30-minute single-step and 24-hour autoregressive rollout). This study is framed as a univariate forecasting framework: predictions are generated solely from the historical CO concentration series without auxiliary meteorological or traffic covariates. On clean data, TSVG-HGBR achieved a 1-step RMSE of 191.84 µg/m 3 (R 2 = 0.971), outperforming both ARIMA (RMSE = 1426; R 2 = − 0.58) and log-transformed SARIMA (RMSE = 1516; R 2 = − 0.78) by approximately 7–8×. On raw (degraded) data, TSVG-HGBR achieved RMSE = 337.81 (R 2 = 0.580), an 8.7% RMSE reduction and 17% R 2 improvement over Baseline HGBR, attributable to the quality-gating mechanism. Systematic fixed-interval evaluation across all non-overlapping windows ( N = 437 clean / 289 raw; step = 48) showed that on clean data TSVG-HGBR recorded lower RMSE in 56.8% of windows (Wilcoxon p = 0.113; not statistically significant). On raw data, Baseline HGBR outperformed TSVG-HGBR in 62.3% of windows (mean paired RMSE difference: +13.45 µg/m 3 ; Wilcoxon p < 0.001), indicating that the single-step quality-gating advantage does not extend to multi-horizon autoregressive forecasting under degraded conditions. SARIMA(log) rollout RMSE (1033 µg/m 3 ) was 1.89× higher than Baseline HGBR, confirming rapid divergence under recursive forecasting. Systematic ablation ( N = 437/289 windows, 7 configurations) identified deg_std and max_degree as the dominant contributors on clean data (+ 19.1% and + 12.9% RMSE when removed; p < 0.001), while the quality score provides the primary independent contribution on raw data (+ 4.3% when removed; p = 0.042). These results establish that quality-gating provides the primary performance gain on degraded sensor data at single-step forecasting horizons, while VG topology features contribute structural discriminators that are dataset-quality-contingent. These findings offer actionable guidance for practitioners deploying ensemble air quality models in IoT sensor environments: prioritize imputation pipeline quality, and use the quality score as a lightweight data-reliability signal.