Consistency of the frequency domain bootstrap for differentiable functionals

Patrice Bertail, Anna E. Dudek

Research output: Contribution to journalArticlepeer-review


In this paper consistency of the Frequency Domain Bootstrap for differentiable functionals of spectral density function of a linear stationary time series is discussed. The notion of influence function in the time domain on spectral measures is introduced. Moreover, the Fréchet and Hadamard differentiability of functionals of spectral measures are defined in the time domain. Sufficient and necessary conditions for consistency of the FDB in the considered problems are provided and the second order correctness is discussed for some functionals. Finally, validity of the FDB for the empirical processes is considered. As an illustration the notions of quantile and range in the time domain are discussed. A simulation study is provided, in which performance of the FDB is analyzed.
Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalElectronic Journal of Statistics
Issue number1
StatePublished - Jan 6 2021
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability


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