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: Faculty of Mathematics, Computer Science and Statistics

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.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Nonparametric Estimation, Lévy Processes, Volatility
• Subjects: 500 Natural sciences and mathematics > 510 Mathematics; 500 Natural sciences and mathematics
• Faculties: Faculty of Mathematics, Computer Science and Statistics
• Language: English
• Date of oral examination: 31. July 2012
• 1. Referee: Mittnik, Stefan
• Signature of the printed copy: 0001/UMC 20550