Empirical spectral processes for locally stationary time series

Details Empirical spectral processes for locally stationary time series Empirical spectral processes for locally stationary time series

2009-02-09

arxiv.org/abs/0902.1448v1

Bernoulli 2009, Vol. 15, No. 1, 1-39

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ137 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

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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