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The Hybrid Wild Bootstrap for Time Series


  • Jens-peter Kreiss
  • Efstathios Paparoditis


We introduce a new and simple bootstrap procedure for general linear processes, called the hybrid wild bootstrap. The hybrid wild bootstrap generates frequency domain replicates of the periodogram that imitate asymptotically correct the first- and second-order properties of the ordinary periodogram including its weak dependence structure at different frequencies. As a consequence, the hybrid wild bootstrapped periodogram succeeds in approximating consistently the distribution of statistics that can be expressed as functionals of the periodogram, including the important class of spectral means for which all so far existing frequency domain bootstrap methods generally fail. Moreover, by inverting the hybrid wild bootstrapped discrete Fourier transform, pseudo-observations in the time domain are obtained. The generated time domain pseudo-observations can be used to approximate correctly the random behavior of statistics, the distribution of which depends on the first-, second-, and, to some extent, on the fourth-order structure of the underlying linear process. Thus, the proposed hybrid wild bootstrap procedure applied to general time series overcomes several of the limitations of standard linear time domain bootstrap methods.

Suggested Citation

  • Jens-peter Kreiss & Efstathios Paparoditis, 2012. "The Hybrid Wild Bootstrap for Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1073-1084, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1073-1084
    DOI: 10.1080/01621459.2012.695664

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    1. repec:bla:jtsera:v:38:y:2017:i:6:p:895-922 is not listed on IDEAS
    2. Maria Fragkeskou & Efstathios Paparoditisāˆ—, 2016. "Inference for the Fourth-Order Innovation Cumulant in Linear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 240-266, March.

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