  This paper tackles one of the most fundamental goals in functional time
series analysis which is to provide reliable predictions for future functions.
Existing methods for predicting a complete future functional observation use
only completely observed trajectories. We develop a new method, called partial
functional prediction (PFP), which uses both completely observed trajectories
and partial information (available partial data) on the trajectory to be
predicted. The PFP method includes an automatic selection criterion for tuning
parameters based on minimizing the prediction error, and the convergence rate
of the PFP prediction is established. Simulation studies demonstrate that
incorporating partially observed trajectory in the prediction outperforms
existing methods with respect to mean squared prediction error. The PFP method
is illustrated to be superior in the analysis of environmental data and traffic
flow data.
