Environmental problems are receiving increasing attention in socio-economic and health studies. This in turn fosters advances in recording and data collection of many related real-life processes. Available tools for data processing are often found too restrictive as they do not account for the rich nature of such data sets. In this paper, we propose a new statistical perspective on forecasting spatial environmental data collected sequentially over time. We treat this data set as a surface (functional) time series with a possibly complicated geographical domain. By employing novel techniques from functional data analysis we develop a new forecasting methodology. Our approach consists of two steps. In the first step, time series of surfaces are reconstructed from measurements sampled over some spatial domain using a finite element spline smoother. In the second step, we adapt the dynamic functional factor model to forecast a surface time series. The advantage of this approach is that we can account for and explore simultaneously spatial as well as temporal dependencies in the data. A forecasting study of ground-level ozone concentration over the geographical domain of Germany demonstrates the practical value of this new perspective, where we compare our approach with standard functional benchmark models.
翻译:在社会经济和健康研究中,环境问题正日益受到社会-经济和健康研究的注意。这反过来又促进了许多相关实际生活过程的记录和数据收集方面的进展。数据处理的现有工具往往被认为限制性过强,因为它们没有考虑到这类数据集的丰富性质。在本文件中,我们提出了预测空间环境数据的新的统计观点,我们把这一数据集视为一个表面(功能)时间序列,其地理范围可能比较复杂。我们利用功能性数据分析的新技术,制定了一个新的预测方法。我们的方法包括两个步骤。第一步,利用一个有限的元素螺旋线平滑器对一些空间域的测量结果进行时间序列的重建。第二步,我们调整了动态功能要素模型,以预测一个表面时间序列。这种方法的优点是,我们可以同时考虑和探索数据中的空间和时间依赖性。对德国地理区域地面臭氧浓度的预测研究显示了这一新观点的实际价值,我们将这一方法与标准功能基准模型进行比较。