Nüßgen, Ines: Ordinal pattern analysis: limit theorems for multivariate long-range dependent Gaussian time series and a comparison to multivariate dependence measur [...]. 2021
Inhalt
- Acknowledgments
- Abstract
- Zusammenfassung
- Contents
- Introduction
- Mathematical preliminaries
- Univariate stochastic processes
- Multivariate stochastic processes
- Gaussian processes
- Framework of Hermite polynomials
- Integrals with respect to random measures
- Spectral representations of stochastic processes
- Integral representations of Hermite-Rosenblatt processes
- Limit theorems for functionals of long-range dependent multivariate Gaussian time series
- Limit theorems for functionals with Hermite rank 1
- Limit theorems for functionals with Hermite rank 2
- Limit theorems for functionals of long-range dependent multivariate Gaussian time series that can be expressed in terms of the increment processes
- Ordinal pattern analysis
- Ordinal patterns
- Ordinal pattern probabilities
- Ordinal pattern dependence
- Limit theorem for the estimator of p in case of long-range dependence
- Limit theorem for the estimator of p in case of short-range dependence
- Limit theorems for estimators of q
- Limit theorems for estimators of ordinal pattern dependence
- Simulation studies
- Adapted and generalized concepts of ordinal pattern dependence
- Estimator of ordinal pattern dependence for a single fixed pattern
- Estimating the Hurst parameters of vector fractional Gaussian noise based on ordinal pattern analysis
- Asymptotics of the estimators of ordinal pattern dependence in case of a stationary time series
- Time shifted estimation of ordinal pattern dependence
- Blockwise estimation of ordinal pattern dependence
- Average-weighted ordinal pattern dependence
- Ordinal pattern dependence in contrast to other measures of dependence
- Approaches of ordinal pattern dependence in comparison to other classical dependence measures: a pilot study
- Comparison: a theoretical approach
- Real-world data analysis
- Conclusion and outlook
- Details of some limit distributions
- Hermite coefficients of n() for h=2 for the pattern =(2,1,0) using the Cholesky decomposition
- Table of Hermite coefficients for n()
- Description of the Matlab algorithms
- Simulation study
- Further information on the real-world data analysis
- Absolute number of pattern in the real-world data analysis for different measuring stations
- Frequency of ordinal patterns for h=1
- Relative frequency of blockwise counted ordinal patterns for h=2
- Ratio of coincident patterns to sample size
- Bibliography
- Notation
- List of Figures
- List of Tables