On projection methods for functional time series forecasting
This work addresses forecasting challenges in functional time series for applications such as energy and environmental monitoring, but it is incremental as it adapts existing projection methods.
The authors tackled forecasting functional time series by proposing two nonparametric methods, including a k-nearest neighbors adaptation and a curve envelope approach, which provided competitive or superior results to benchmarks on simulated and real-world data like electricity demand and NOx emissions.
Two nonparametric methods are presented for forecasting functional time series (FTS). The FTS we observe is a curve at a discrete-time point. We address both one-step-ahead forecasting and dynamic updating. Dynamic updating is a forward prediction of the unobserved segment of the most recent curve. Among the two proposed methods, the first one is a straightforward adaptation to FTS of the $k$-nearest neighbors methods for univariate time series forecasting. The second one is based on a selection of curves, termed \emph{the curve envelope}, that aims to be representative in shape and magnitude of the most recent functional observation, either a whole curve or the observed part of a partially observed curve. In a similar fashion to $k$-nearest neighbors and other projection methods successfully used for time series forecasting, we ``project'' the $k$-nearest neighbors and the curves in the envelope for forecasting. In doing so, we keep track of the next period evolution of the curves. The methods are applied to simulated data, daily electricity demand, and NOx emissions and provide competitive results with and often superior to several benchmark predictions. The approach offers a model-free alternative to statistical methods based on FTS modeling to study the cyclic or seasonal behavior of many FTS.