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

## TL;DR

This paper introduces a novel partial functional prediction method that leverages both complete and partial trajectory data to improve future function predictions in functional time series analysis.

## Contribution

The paper develops the PFP method, which incorporates partial observations and includes an automatic tuning criterion, with proven convergence rates.

## Key findings

- PFP outperforms existing methods in simulation studies.
- Incorporating partial data improves prediction accuracy.
- Method is effective in environmental and traffic flow data analysis.

## Abstract

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.