Enhancing air quality forecasting through missing data imputation: a stacking-based approach applied to urban monitoring data

In air pollution forecasting, handling missing data is a significant challenge and a crucial task. In this study, we aim to forecast air pollutants in Eskişehir, Türkiye, presenting a new stacking-based imputation method (S-UImpute) to address the missing data problem. To this end, we apply three widely used forecasting methods: Autoregressive Integrated Moving Average (ARIMA), Support Vector Regression (SVR), and Long Short-Term Memory (LSTM), and eight commonly used missing data imputation methods (ZeroFill, MeanFill, MedianFill, ForwardFill, BackwardFill, Interpolation, Kalman filtering, and SVR-based imputation) for benchmarking on univariate time series data. We collect comprehensive datasets, which have various proportions of missing data, from five air quality monitoring stations in Eskişehir. To evaluate the performance of the proposed method at high missing data rates, we generated artificial missing data on top of the existing missing data at rates of 10%, 15%, 20%, and 25%. The S-UImpute + LSTM model mostly outperformed the other imputation method and forecasting model combinations in terms of modified symmetric Mean Absolute Percentage Error (msMAPE). Moreover, S-UImpute provided more consistent and generalized performance compared with other imputation methods. As LSTM produced the most accurate forecasting, it is used to statistically compare imputation methods and determine the best-performing one. According to the Friedman statistical test, there is a statistically significant difference between the missing data imputation methods. Following this, the Wilcoxon signed-rank test applied afterwards indicates that the best method is S-UImpute.