Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration

Environmental data often take the form of a collection of curves observed sequentially over time. An example of this includes daily pollution measurement curves describing the concentration of a particulate matter in ambient air. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. The nature of high-dimensional data poses challenges from a statistical aspect, due to the so-called “curse of dimensionality”, but it also poses opportunities to analyze a rich source of information to better understand dynamic changes at short time intervals. Statistical methods are introduced and compared for forecasting one-day-ahead intraday concentrations of particulate matter; as new data are sequentially observed, dynamic updating methods are proposed to update point and interval forecasts to achieve better accuracy. These forecasting methods are validated through an empirical study of half-hourly concentrations of airborne particulate matter in Graz, Austria.