Open Access
December 2018 Sieve bootstrap for functional time series
Efstathios Paparoditis
Ann. Statist. 46(6B): 3510-3538 (December 2018). DOI: 10.1214/17-AOS1667

Abstract

A bootstrap procedure for functional time series is proposed which exploits a general vector autoregressive representation of the time series of Fourier coefficients appearing in the Karhunen–Loève expansion of the functional process. A double sieve-type bootstrap method is developed, which avoids the estimation of process operators and generates functional pseudo-time series that appropriately mimics the dependence structure of the functional time series at hand. The method uses a finite set of functional principal components to capture the essential driving parts of the infinite dimensional process and a finite order vector autoregressive process to imitate the temporal dependence structure of the corresponding vector time series of Fourier coefficients. By allowing the number of functional principal components as well as the autoregressive order used to increase to infinity (at some appropriate rate) as the sample size increases, consistency of the functional sieve bootstrap can be established. We demonstrate this by proving a basic bootstrap central limit theorem for functional finite Fourier transforms and by establishing bootstrap validity in the context of a fully functional testing problem. A novel procedure to select the number of functional principal components is introduced while simulations illustrate the good finite sample performance of the new bootstrap method proposed.

Citation

Download Citation

Efstathios Paparoditis. "Sieve bootstrap for functional time series." Ann. Statist. 46 (6B) 3510 - 3538, December 2018. https://doi.org/10.1214/17-AOS1667

Information

Received: 1 September 2016; Revised: 1 September 2017; Published: December 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06965696
MathSciNet: MR3852660
Digital Object Identifier: 10.1214/17-AOS1667

Subjects:
Primary: 62M10 , 62M15
Secondary: 62G09

Keywords: bootstrap , Fourier transform , Karhunen–Loève expansion , principal components , spectral density operator

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 6B • December 2018
Back to Top