Quantile-based spectral analysis: asymptotic theory and computation. In this thesis an alternative method for the spectral analysis of a strictly stationary time series is presented. Measures for serial dependence based on copulas or joint distributions of pairs of observations of lag $k$ are introduced. These measures allow for separation of marginal from serial aspects of a time series and completely describe the distributions of all pairs of observations, respectively. With respect to the information they provide about the conditional distribution the new approach clearly outreaches the traditional, covariance-based one. The new spectrum is made statistically tractable by the definition of two types of estimators. Results about the consistency and asymptotic distribution of smoothed versions of these estimators are proven. An object-oriented framework for computation of the new statistics is documented and the developed R-package “quantspec” is used to perform simulation studies illustrating the potential for empirical applications.
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References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Chen, Tianbo; Sun, Ying; Li, Ta-Hsin: A semi-parametric estimation method for the quantile spectrum with an application to earthquake classification using convolutional neural network (2021)
- Zhang, Shibin: Bayesian copula spectral analysis for stationary time series (2019)
- Kley, Tobias; Volgushev, Stanislav; Dette, Holger; Hallin, Marc: Quantile spectral processes: asymptotic analysis and inference (2016)
- Tobias Kley: Quantile-Based Spectral Analysis in an Object-Oriented Framework and a Reference Implementation in R: The quantspec Package (2016) not zbMATH
- Kley, Tobias: Quantile-based spectral analysis: asymptotic theory and computation (2014)