Exact simulation of Gaussian Time Series from Nonparametric Spectral Estimates with Application to Bootstrapping |
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Authors: | Donald B Percival William L B Constantine |
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Institution: | (1) Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640, USA;(2) Constantine Insightful Corporation, 1700 Westlake Avenue North, Suite 500, Seattle, WA 98109-9891, USA |
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Abstract: | 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. |
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Keywords: | Circulant embedding Gaussian process Power law process Surrogate time series Time series analysis |
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