On projection methods for functional time series forecasting

Antonio Elías*, Raúl Jiménez, Han Lin Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
64 Downloads (Pure)


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.
Original languageEnglish
Article number104890
Pages (from-to)1-13
Number of pages13
JournalJournal of Multivariate Analysis
Early online date3 Nov 2021
Publication statusPublished - May 2022

Bibliographical note

© 2021 The Author(s). Published by Elsevier Inc. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Forecasting
  • Functional depth
  • Functional nonparametric
  • Functional time series
  • Nearest neighbors


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