Incorporating model uncertainty in the construction of bootstrap prediction intervals for functional time series

Efstathios Paparoditis, Hanlin Shang*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

A sieve bootstrap method that incorporates model uncertainty for constructing pointwise or simultaneous prediction intervals of stationary functional time series is proposed. The bootstrap method exploits a general backward vector autoregressive representation of the time series of Fourier coefficients appearing in the well-established Karhunen-Loève expansion of the functional process. The bootstrap method generates, by running backward in time, functional bootstrap samples which adequately mimic the dependence structure of the underlying process and which all have the same conditionally fixed curves at the end of every functional bootstrap sample. The bootstrap prediction error distribution is then calculated as the difference between the model-free bootstrap generated future functional pseudo-observations and the functional forecasts obtained from a model used for prediction. In this way, the estimated prediction error distribution takes into account not only the innovation and estimation error associated with prediction, but also the possible error due to model uncertainty or misspecification. Through a simulation study, we demonstrate an excellent finite-sample performance of the proposed sieve bootstrap method.
Original languageEnglish
Title of host publicationNonparametric Statistics
Subtitle of host publication4th ISNPS, Salerno, Italy, June 2018
EditorsMichele La Rocca, Brunero Liseo, Luigi Salmaso
Place of PublicationSalerno
PublisherSpringer, Springer Nature
Pages415-422
Number of pages8
ISBN (Electronic)9783030573065
ISBN (Print)9783030573058
DOIs
Publication statusPublished - 2020
EventConference of the International Society for Nonparametric Statistics (4th : 2018) - Salerno, Italy
Duration: 11 Jun 201815 Jun 2018

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume339
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceConference of the International Society for Nonparametric Statistics (4th : 2018)
CountryItaly
CitySalerno
Period11/06/1815/06/18

Keywords

  • Fourier transform
  • Functional prediction
  • Karhunen-Loéve expansion
  • Prediction error
  • Principal components

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