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November 2009 Testing temporal constancy of the spectral structure of a time series
Efstathios Paparoditis
Bernoulli 15(4): 1190-1221 (November 2009). DOI: 10.3150/08-BEJ179


Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.


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Efstathios Paparoditis. "Testing temporal constancy of the spectral structure of a time series." Bernoulli 15 (4) 1190 - 1221, November 2009.


Published: November 2009
First available in Project Euclid: 8 January 2010

zbMATH: 1200.62049
MathSciNet: MR2597589
Digital Object Identifier: 10.3150/08-BEJ179

Rights: Copyright © 2009 Bernoulli Society for Mathematical Statistics and Probability


Vol.15 • No. 4 • November 2009
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