Empirical spectral processes for locally stationary time series

Rainer Dahlhaus and Wolfgang Polonik

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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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Bernoulli, Volume 15, Number 1 (2009), 1-39.

First available in Project Euclid: 3 February 2009

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asymptotic normality empirical spectral process locally stationary processes non-stationary time series quadratic forms


Dahlhaus, Rainer; Polonik, Wolfgang. Empirical spectral processes for locally stationary time series. Bernoulli 15 (2009), no. 1, 1--39. doi:10.3150/08-BEJ137.

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