Estimation and Testing of the Jump Component in Levy Processes

In this thesis, a new method based on characteristic functions is proposed to estimate the jump component in a finite-activity Levy process, which includes the jump frequency and the jump size distribution. Properties of the estimators are investigated, which show that this method does not require high frequency data. The implementation of the method is discussed, and examples are provided. We also perform a comparison which shows that our method has advantages over an existing threshold method. Finally, two applications are included: one is the classification of the increments of the model, and the other is the testing for a change of jump frequency.