A novel framework for stacked regression based on machine learning was developed to predict the daily average concentrations of particulate matter (PM₁₀), one of Bulgaria’s primary health concerns. The measurements of nine meteorological parameters were introduced as independent variables. The goal was to carefully study a limited number of initial predictors and extract stochastic information from them to build an extended set of data that allowed the creation of highly efficient predictive models. Four base models using random forest, CART ensemble and bagging, and their rotation variants, were built and evaluated. The heterogeneity of these base models was achieved by introducing five types of diversities, including a new simplified selective ensemble algorithm. The predictions from the four base models were then used as predictors in multivariate adaptive regression splines (MARS) models. All models were statistically tested using out-of-bag or with 5-fold and 10-fold cross-validation. In addition, a variable importance analysis was conducted. The proposed framework was used for short-term forecasting of out-of-sample data for seven days. It was shown that the stacked models outperformed all single base models. An index of agreement IA = 0.986 and a coefficient of determination of about 95% were achieved.

In this study, a novel general multi-step ahead strategy is developed for forecasting time series of air pollutants. The values of the predictors at future moments are gathered from official weather forecast sites as independent ex-ante data. They are updated with new forecasted values every day. Each new sample is used to build- a separate single model that simultaneously predicts future pollution levels. The sought forecasts were estimated by averaging the actual predictions of the single models. The strategy was applied to three pollutants—PM₁₀, SO₂, and NO₂—in the city of Pernik, Bulgaria. Random forest (RF) and arcing (Arc-x4) machine learning algorithms were applied to the modeling. Although there are many highly changing day-to-day predictors, the proposed averaging strategy shows a promising alternative to single models. In most cases, the root mean squared errors (RMSE) of the averaging models (aRF and aAR) for the last 10 horizons are lower than those of the single models. In particular, for PM₁₀, the aRF’s RMSE is 13.1 vs. 13.8 micrograms per cubic meter for the single model; for the NO₂ model, the aRF exhibits 21.5 vs. 23.8; for SO_2, the aAR has 17.3 vs. 17.4; for NO₂, the aAR’s RMSE is 22.7 vs. 27.5, respectively. Fractional bias is within the same limits of (−0.65, 0.7) for all constructed models.