Nonparametric estimation of the jump component in financial time series

Yener, Serkan (2012): Nonparametric estimation of the jump component in financial time series. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

Abstract

In this thesis, we analyze nonparametric estimation of Lévy-based models using wavelets methods. As the considered class is restricted to pure-jump Lévy processes, it is sufficient to estimate their Lévy densities. For implementing a wavelet density estimator, it is necessary to setup a preliminary histogram estimator. Simulation studies show that there is an improvement of the wavelet estimator by invoking an optimally selected histogram. The wavelet estimator is based on block-thresholding of empirical coefficients. We conclude with two empirical applications which show that there is a very high arrival rate of small jumps in financial data sets.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Nonparametric Estimation, Lévy Processes, Volatility
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik ; 500 Naturwissenschaften und Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 31. Juli 2012
• 1. Bericht­erstatter:in: Mittnik, Stefan