Functional time series prediction under partial observation of the future curve

This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for functions. Existing functional time series methods seek to predict a complete future functional observation based on a set of observed complete trajectories. 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. To solve this problem, we propose a new method "partial functional prediction (PFP)". The proposed method combines "next-interval" prediction and fully functional regression prediction, so that the partially observed part of the trajectory can aid in producing a better prediction for the unobserved part of the future curve. In PFP, we include automatic selection criterion for tuning parameters based on minimizing the prediction error. Simulations indicate that the proposed method can outperform existing methods with respect to mean-square prediction error and its practical utility is illustrated in an analysis of environmental and traffic flow data.