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

arXiv: https://arxiv.org/abs/1906.00281 · HTML: https://mlsanity.com/paper/1906.00281/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Conformal Prediction Bands for Two-Dimensional Functional Time Series](https://mlsanity.com/paper/2207.13656/) (2022)
- [Coefficient Shape Alignment in Multiple Functional Linear Regression](https://mlsanity.com/paper/2312.01925/) (2023)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (2025)
- [Probabilistic Functional Neural Networks](https://mlsanity.com/paper/2503.21585/) (2025)
- [Coefficient Shape Transfer Learning for Functional Linear Regression](https://mlsanity.com/paper/2506.11367/) (2025)

## Abstract (arXiv)

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.