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February 2009 Empirical spectral processes for locally stationary time series
Rainer Dahlhaus, Wolfgang Polonik
Bernoulli 15(1): 1-39 (February 2009). DOI: 10.3150/08-BEJ137


A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a Glivenko–Cantelli-type convergence result. The results use conditions based on the metric entropy of the index class. In contrast to related earlier work, no Gaussian assumption is made. As applications, quasi-likelihood estimation, goodness-of-fit testing and inference under model misspecification are discussed. In an extended application, uniform rates of convergence are derived for local Whittle estimates of the parameter curves of locally stationary time series models.


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Rainer Dahlhaus. Wolfgang Polonik. "Empirical spectral processes for locally stationary time series." Bernoulli 15 (1) 1 - 39, February 2009.


Published: February 2009
First available in Project Euclid: 3 February 2009

zbMATH: 1204.62156
MathSciNet: MR2546797
Digital Object Identifier: 10.3150/08-BEJ137

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


Vol.15 • No. 1 • February 2009
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