Statistics and Computing

, Volume 16, Issue 1, pp 25–35 | Cite as

Exact simulation of Gaussian Time Series from Nonparametric Spectral Estimates with Application to Bootstrapping

  • Donald B. Percival
  • William L. B. Constantine


The circulant embedding method for generating statistically exact simulations of time series from certain Gaussian distributed stationary processes is attractive because of its advantage in computational speed over a competitive method based upon the modified Cholesky decomposition. We demonstrate that the circulant embedding method can be used to generate simulations from stationary processes whose spectral density functions are dictated by a number of popular nonparametric estimators, including all direct spectral estimators (a special case being the periodogram), certain lag window spectral estimators, all forms of Welch's overlapped segment averaging spectral estimator and all basic multitaper spectral estimators. One application for this technique is to generate time series for bootstrapping various statistics. When used with bootstrapping, our proposed technique avoids some – but not all – of the pitfalls of previously proposed frequency domain methods for simulating time series.


Circulant embedding Gaussian process Power law process Surrogate time series Time series analysis 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Donald B. Percival
    • 1
  • William L. B. Constantine
    • 2
  1. 1.Applied Physics LaboratoryUniversity of WashingtonSeattleUSA
  2. 2.Constantine Insightful CorporationSeattleUSA

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