Functional Time Series Prediction Under Partial Observation of the Future Curve

Abstract

Abstract–This article 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.

KEYWORDS:

• Dimension reduction
• Functional principal component
• Final prediction error
• Functional time series
• Intra-day fully functional linear regression model
• Long-term and short-term dynamics
• Updating prediction

Supplementary Material

The supplementary material contains the technical derivation of the fFPE criterion, the proofs of the theorems and the additional simulation results on the bootstrap prediction interval.