We present a method to forecast pollution episodes with a bivariate response. The method simultaneously estimates the concentrations of two pollutants, using historical data. It is based on a location–scale model where the means and the standard deviations are approximated by kernel smoothers in additive models, while the variance–covariance matrix is obtained from the residuals of the previous models. The method provides not only an estimation of the concentration of both pollutants over time but also uncertainty regions covering a specific percentage of the data. The suitability of the model was tested with both simulated and real data (specifically \(\hbox {SO}_2\) and \(\hbox {NO}_x\) concentrations from a coal-fired power station). The results have proved highly satisfactory in both cases. The percentage of data covered by the uncertainty region, its area and a new loss function, a variant of the pinball loss function, were used as metrics to evaluate the performance of the model.

我们提出了一种预测具有双变量响应的污染事件的方法。该方法使用历史数据同时估算两种污染物的浓度。它基于位置尺度模型，其中均值和标准差通过加性模型中的核平滑器进行近似，而方差-协方差矩阵是从先前模型的残差中获得的。该方法不仅可以估算出两种污染物随时间的浓度，还可以提供覆盖特定百分比数据的不确定区域。使用模拟和真实数据（特别是\（\ hbox {SO} _2 \）和\（\ hbox {NO} _x \）对模型的适用性进行了测试燃煤发电站的浓度）。两种情况下的结果均被证明是非常令人满意的。不确定性区域，其面积和新的损失函数（弹球损失函数的一种变体）所覆盖的数据百分比用作评估模型性能的指标。