Forecasting Environmental Data: An example to ground-level ozone concentration surfaces

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.