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Bootstrap methods for stationary functional time series

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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 (\(\hbox {PM}_{10}\)) dataset in Graz, the proposed bootstrap methods provide a way of constructing the distribution of estimated long-run covariance for functional time series.

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Acknowledgments

The author would like to thank insightful comments and suggestions provided by two reviewers and the participants at the session titled “Resampling procedures for dependent data” of the \(8\hbox {th}\) International Conference of the ERCIM WG on Computational and Methodological Statistics held in London in December 2015.

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  1. Research School of Finance, Actuarial Studies and Statistics, Australian National University, Level 4, Building 26C, Kingsley Street, Acton, ACT, 2601, Australia

    Han Lin Shang

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  1. Han Lin Shang
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Correspondence to Han Lin Shang.

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Shang, H.L. Bootstrap methods for stationary functional time series. Stat Comput 28, 1–10 (2018). https://doi.org/10.1007/s11222-016-9712-8

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