Bootstrap methods for stationary functional time series

TL;DR

This paper introduces and compares three bootstrap methods for estimating the long-run covariance in stationary functional time series, using functional principal component analysis, sieve, and kernel regression, validated through simulations and real data.

Contribution

It proposes a versatile bootstrap approach based on functional principal components and compares it with sieve and kernel methods for functional time series.

Findings

Bootstrap methods perform well in finite samples.

Functional principal component bootstrap is flexible and effective.

Methods successfully applied to real particulate matter data.

Abstract

Bootstrap methods for estimating the long-run covariance of stationary functional time series are considered. We introduce a versatile bootstrap method that relies on functional principal component analysis, where principal component scores can be bootstrapped by maximum entropy. Two other bootstrap methods resample error functions, after the dependence structure being modeled linearly by a sieve method or nonlinearly by a functional kernel regression. Through a series of Monte-Carlo simulation, we evaluate and compare the finite-sample performances of these three bootstrap methods for estimating the long-run covariance in a functional time series. Using the intraday particulate matter (PM10) data set in Graz, the proposed bootstrap methods provide a way of constructing the distribution of estimated long-run covariance for functional time series.