Bibliographic Metadata
Bibliographic Metadata
- TitleNew developments of parametric and semiparametric volatility models with application to quantitative risk management / von Sebastian Letmathe
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- Description1 Online-Ressource (VI, 11 Seiten, Seite 159-179) : Diagramme
- Institutional NoteUniversität Paderborn, Dissertation, 2023
- AnnotationTag der Verteidigung: 20.02.2023
- Defended on2023-02-20
- LanguageEnglish
- Document TypesDissertation (PhD)
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Abstract
The underlying methodology of this thesis is based on the decomposition of a time series into a deterministic and stochastic component, where the latter is assumed to follow well-known time series models from the ARMA- as well as GARCH-class and the formeris a non-negative slowly varying function, which can be estimated via a nonparametric smoothing method. A time series composed as described before is at best locally stationary. Hence, fitting a parametric model directly to such a series is in fact a misspecication. As a remedy, the deterministic trend or scale function has to be estimated and removed beforehand from the data, in order to fit a parametric model to the approximately stationary residuals. In this thesis local polynomial and penalised spline regression are employed for the estimation of the deterministic component. Various iterative plug-in algorithms are proposed for smoothing parameter selection and are implemented in R-packages, namely smoots, esemifar and ufRisk. All these packages are publicly available on CRAN. The wide applicability of these packages is illustrated with real data examples and the performance of the algorithms is validated within the scope of thorough simulation studies. One of the major contributions of this thesis is the development and application of a new parametric time series model with long memory, namely the FI-Log-GARCH and various semiparametric extensions of this model as well as of other well-known time series models with short- and long memory. The FI-Log-GARCH is a fractional extension of the Log-GARCH. Theoretical properties such as necessary and sucient conditions for stationary solutions, existence of nite fourth moments, explicit expression for the autocorrelation and central limit theorem for the sample mean are derived.
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