# On projection methods for functional time series forecasting

arXiv: https://arxiv.org/abs/2105.04399 · HTML: https://mlsanity.com/paper/2105.04399/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 80 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 7 of 7)

- [Extremal Depth for Functional Data and Applications](https://mlsanity.com/paper/1511.00128/) (2015)
- [Multivariate Functional Data Visualization and Outlier Detection](https://mlsanity.com/paper/1703.06419/) (2017)
- [Modelling and forecasting daily electricity load curves: a hybrid approach](https://mlsanity.com/paper/1611.08632/) (2016)
- [The DDG-classifier in the functional setting](https://mlsanity.com/paper/1501.00372/) (2015)
- [Functional Time Series](https://mlsanity.com/paper/1502.07113/) (2015)
- [An Innovations Algorithm for the prediction of functional linear processes](https://mlsanity.com/paper/1607.05874/) (2016)
- [Scalar-on-function local linear regression and beyond](https://mlsanity.com/paper/1907.08074/) (2019)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Functional Neural Networks](https://mlsanity.com/paper/2503.21585/) (2025)

## Abstract (arXiv)

Two nonparametric methods are presented for forecasting functional time series (FTS). The FTS we observe is a curve at a discrete-time point. We address both one-step-ahead forecasting and dynamic updating. Dynamic updating is a forward prediction of the unobserved segment of the most recent curve. Among the two proposed methods, the first one is a straightforward adaptation to FTS of the k-nearest neighbors methods for univariate time series forecasting. The second one is based on a selection of curves, termed the curve envelope, that aims to be representative in shape and magnitude of the most recent functional observation, either a whole curve or the observed part of a partially observed curve. In a similar fashion to k-nearest neighbors and other projection methods successfully used for time series forecasting, we ``project'' the k-nearest neighbors and the curves in the envelope for forecasting. In doing so, we keep track of the next period evolution of the curves. The methods are applied to simulated data, daily electricity demand, and NOx emissions and provide competitive results with and often superior to several benchmark predictions. The approach offers a model-free alternative to statistical methods based on FTS modeling to study the cyclic or seasonal behavior of many FTS.