Empirical spectral processes for locally stationary time series
By Rainer Dahlhaus, Wolfgang Polonik. 2009
118 citations recorded by the source corpus.
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, prove a maximal exponential inequality and a Glivenko-Cantelli type convergence result. The results use conditions based on 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.
Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6d156362e8f2b9cdf2f009f0cff76d01d3c253b2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Stanislav Volgushev
- Holger Dette
- Tobias Kley
- Marc Hallin
- Stefan Birr
- Rainer Dahlhaus
- S. Rao
- Johan Segers
In Statistical and Nonlinear Physics
In Statistics and Probability
- Stanislav Volgushev
- Holger Dette
- Marc Hallin
- Tobias Kley
- Stefan Birr
- Rainer Dahlhaus
- Davy Paindaveine
- R. von Sachs
Citations in the corpus
- Quantile spectral analysis for locally stationary time series (2014, background): “t varying-parameter autoregressive models; so is Dahlhaus et al. (1999); Dahlhaus (1997) is based on time-varying (second-order) spectral representations, turned into time-domain linear MA(1) ones by Dahlhaus and Polonik (2009); Dahlhaus and Subba Rao (2006) and Fryzlewicz et al. (2008) deal with lo”
- Quantile Spectral Processes: Asymptotic Analysis and Inference (2014, unknown): “For more details, see Dahlhaus [8], Dahlhaus and Polonik [9], and the references therein.”
- Locally Stationary Processes (2011, background): “Tightness and therefore the functional convergence follows from Theorem 2.11 of Dahlhaus and Polonik (2009).”