Bootstrap methods for stationary functional time series

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24 Citations (Scopus)


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) dataset in Graz, the proposed bootstrap methods provide a way of constructing the distribution of estimated long-run covariance for functional time series.
Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalStatistics and Computing
Issue number1
Publication statusPublished - 8 Jan 2018
Externally publishedYes


  • Maximum entropy
  • Functional principal component analysis
  • Functional autoregressive process
  • Functional kernel regression
  • Long-run covariance
  • Plug-in bandwidth


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