Graph features boost short-term urban CO forecasting, not full-day prediction

A hybrid forecasting system that combines network-based features of carbon monoxide time series with a signal indicating how complete recent observations are achieved substantially better 30-minute predictions from a sensor record with missing data, but its advantage does not survive a full 24-hour recursive forecast. The study tested the TSVG-HGBR framework on 105,216 half-hourly carbon monoxide measurements recorded at a monitoring station in Semarang, Indonesia, from January 2019 through December 2024. About 24.5% of the raw measurements were missing. On the degraded data, TSVG-HGBR produced a root mean squared error of 337.81 micrograms per cubic metre for the next 30 minutes, an 8.7% reduction from the 370.12 micrograms per cubic metre obtained by a gradient-boosting model using only recent concentration values. Its coefficient of determination, R², rose from 0.4958 to 0.5800. The result shows that explicitly telling an algorithm how reliable its input window is can improve immediate forecasts drawn from an imperfect environmental sensor stream.

The framework is designed as a univariate, single-station model: every prediction comes from the historical carbon monoxide series, without weather, traffic, spatial or other sensor information. For each 24-observation window, corresponding to 12 hours at the station’s sampling interval, the researchers constructed a Natural Visibility Graph. Each observation becomes a node, and two nodes are linked when the values between them remain below the straight line joining them. The resulting topology summarizes the shape of the recent trajectory without relying only on conventional time lags. Four quantities were extracted: average node degree, graph density, the standard deviation of degree and the maximum degree. These were concatenated with the previous 24 carbon monoxide measurements and a quality score, defined as one minus the proportion of missing values in the window, to form a 29-feature input for a Histogram-based Gradient Boosting Regressor.

The study used a strictly chronological 80% training and 20% testing split, so later observations were not mixed into earlier training sets. Two data conditions were examined. The first, called clean data, had missing values filled by K-nearest-neighbours interpolation with temporal distance weighting and five neighbours. The second retained the original gaps to represent field conditions involving sensor downtime, calibration and communication failures. Model hyperparameters were selected through 100 Optuna trials using a 20% chronological holdout. On clean data, TSVG-HGBR achieved an RMSE of 191.84 micrograms per cubic metre and an R² of 0.971 for the 30-minute forecast. It was only slightly better than the lag-only boosting model, which recorded an RMSE of 192.81, a 0.5% difference. By contrast, ARIMA(2,1,1) and a log-transformed seasonal ARIMA model performed poorly, with RMSE values of about 1,426 and 1,516 micrograms per cubic metre and negative R² values.

The stronger result on the raw series came from the quality score. Because every window in the clean dataset is complete after imputation, that feature is always 1 and provides no additional discrimination. In raw windows, however, it varies continuously according to local completeness, allowing the boosting model to distinguish observations drawn from well-covered periods from those surrounded by gaps. This difference is important because the clean-data result is partly optimistic: predictions are evaluated against KNN-imputed target values, so residual imputation error is not fully penalised. On raw data, predictions are compared with sensor readings at non-missing target times, and windows with missing targets are excluded. The reported clean-data RMSE is therefore not directly equivalent to an error measure against an entirely observed target, even though both conditions use the same model and evaluation design.

The researchers also tested a 24-hour forecast horizon through 48 autoregressive steps. At each step, the model’s prediction was inserted into the moving window, the oldest value was removed, and a new visibility graph and set of features were generated. In one illustrative raw-data rollout, the lag-only model diverged to an RMSE of 10,328.22 micrograms per cubic metre, while TSVG-HGBR remained at 4,849.82. That striking snapshot did not represent the general case, however. A systematic evaluation using all eligible non-overlapping 48-step windows assessed 437 clean-data rollouts and 289 raw-data rollouts. On clean data, TSVG-HGBR had lower RMSE in 56.8% of windows, but the difference from the baseline was not statistically significant, with a Wilcoxon p-value of 0.113. Its mean RMSE was actually higher, at 578.97 compared with 545.55 micrograms per cubic metre, because it underperformed in a subset of windows.

The raw-data rollout reversed that pattern. The baseline boosting model had lower mean RMSE, 551.09 compared with 564.54 micrograms per cubic metre, and performed better in 62.3% of the 289 windows; the paired difference was statistically significant at p below 0.001. Median RMSE values were nearly identical—602.90 for the baseline and 602.61 for TSVG-HGBR—suggesting that the quality-aware model may limit extreme failures without improving typical 24-hour performance. The seasonal statistical baseline was less successful still, with a mean rollout RMSE of 1,033.01 micrograms per cubic metres, 1.89 times the baseline value. These findings make the practical boundary clear: the method’s 8.7% advantage for a 30-minute forecast on degraded data does not constitute a demonstrated advantage for a full-day recursive forecast.

Ablation experiments helped explain why the results changed. The researchers removed one feature at a time and repeated the systematic rollout evaluation across seven configurations. In clean data, removing degree standard deviation increased mean RMSE by 19.1%, while removing maximum degree increased it by 12.9%; both changes were significant at p below 0.001. Average degree and density produced no independent improvement and were mathematically redundant at the fixed window size. Indeed, removing all visibility-graph features did not significantly worsen clean-data rollout performance. In raw data, the pattern differed. Removing the full graph-feature set increased mean RMSE by 11.2% at p below 0.001, while removing the quality score alone increased RMSE by 4.3% at p = 0.042. Thus, the reliability score supplied the clearest independent benefit under degradation, whereas particular graph metrics mattered most when windows were complete.

Missing values also altered the graphs themselves. A Natural Visibility Graph requires ordered, defined observations; when values are absent, nodes representing those gaps can acquire zero visibility, suppressing connectivity and producing graph metrics unlike those learned from complete windows. The quality score appears to provide a corrective signal in this setting, but it cannot fully prevent the graph structure from deteriorating. During recursive forecasting, another distribution shift emerges: later windows contain a growing mixture of model predictions and observed values, whereas the model was trained on graph features derived from historical observations. The authors note that accumulated error can therefore corrupt both the lag inputs and subsequent graph construction. The systematic results, rather than the exceptional single-window example, support the conclusion that the extra structural machinery does not yet provide a reliable 24-hour advantage in degraded data.

Several limitations constrain how broadly the findings can be applied. The study covers one station in one city, so urban carbon monoxide patterns elsewhere may produce different graph distributions. Hyperparameters were optimized on the clean data but not separately for the raw scenario, and the evaluation did not include deep-learning models such as long short-term memory or gated recurrent-unit networks. The framework also omits meteorological and traffic covariates, even though these could materially affect carbon monoxide dynamics. Most significantly, the KNN preprocessing has difficulty with long consecutive gaps: it falls back to a weighted mean of distant valid observations, creates spatially constant estimates within long masked blocks and systematically underestimates high-concentration episodes. In the 2019 data, 68.6% of the record was missing. These preprocessing problems mean that the impressive clean-data performance partly reflects reconstructed values as well as forecast skill. The evidence supports a focused conclusion: visibility-graph features can sharpen immediate urban carbon monoxide forecasts and a simple completeness score helps at the next 30-minute step, but neither has yet demonstrated a dependable advantage over lag-only gradient boosting across repeated 24-hour forecasts from incomplete sensor records.

Subject of Research: Evaluation of a visibility-graph and gradient-boosting model for urban carbon monoxide forecasting

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

Article References: Sugiharto, W. H., Bardadi, A., Ghozali, M. I., Sukri, H., & Murti, A. C. (2026). Time-series visibility graph and histogram-based gradient boosting regressor (TSVG-HGBR) for robust multi-horizon urban carbon monoxide forecasting. Discover Artificial Intelligence, 6(1), Article 1207. https://doi.org/10.1007/s44163-026-02286-w

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02286-w

Keywords: carbon monoxide forecasting, visibility graphs, gradient boosting, urban air quality, sensor missing data, data quality, autoregressive forecasting, imputation, time series analysis, Semarang, Time-series, visibility