Functional time series prediction under partial observation of the future curve.

Providing reliable predictions is one of the fundamental topics in functional time series analysis. Existing functional time series methodology seeks to predict a complete future functional observation based on a set of observed functions. The problem of interest discussed here is how to advance prediction methodology to cases where partial information on the next trajectory is available, with the aim of improving prediction accuracy. The proposed method combines "next-interval" prediction and fully functional regression prediction, so that the partially observed part can aid in producing a better guess for the unobserved part of the future curve. An automatic selection criterion based on minimizing the prediction error helps select unknown tuning parameters. Simulations indicate that the proposed method can outperform existing methods with respect to mean-square prediction error of the unobserved part, and its practical usefulness is illustrated in an analysis of environmental and traffic flow data.