We introduce a spatio-temporal model to represent development of atmospheric pollution in an urban area. An important element of this is that recorded measurements are often incomplete which undermines time-series approaches. We identify the multiple imputation by chained equation (MICE) method as effective to complete data sequences synthetically. Following on from this, we develop a vector autoregressive moving average (VARMA) model for the spatio-temporal development of atmospheric pollution in urban areas. This model was fitted to hourly measurements of four pollutants (NO, NO₂, NO_x and PM₁₀) for the whole of the calendar year 2017 at 30 stations across London, completed by MICE as required. We show by cross-validation that the VARMA model is more effective than other formulations, including the Kriging method of spatial interpolation, and seasonal ARMA models for individual stations with either daily or weekly trends. The resulting model can be used for prediction of air quality in different periods and as the basis for assessment of policy interventions such as increasing vehicle emission standards, and traffic management and control policies such as low and ultra-low emission zones.

我们引入时空模型来代表市区大气污染的发展。其中一个重要因素是，记录的测量值通常不完整，这会破坏时间序列方法。我们确定通过链式方程（MICE）方法进行的多重插补有效地完成了数据序列的合成。在此基础上，我们针对城市大气污染的时空发展建立了矢量自回归移动平均（VARMA）模型。该模型适合每小时测量四种污染物（NO，NO ₂，NO _x和PM ₁₀），整个2017日历年在伦敦的30个站点进行，由MICE按要求完成。通过交叉验证，我们证明了VARMA模型比其他公式更有效，包括空间插值的Kriging方法以及具有每日或每周趋势的单个站点的季节性ARMA模型。所得模型可用于预测不同时期的空气质量，并可作为评估政策干预措施（例如提高车辆排放标准）以及交通管理和控制政策（例如低排放区和超低排放区）的基础。