Jumps Activity and Singularity Spectra for Instruments in the Polish Financial Market

Abstract

In the paper we try to measure the activity of jumps in returns of some instruments from the Polish financial market. We use Blumenthal-Getoor index β for Levy processes as a measure of jumps’ activity. This allows us to distinguish between processes with rare and sharp jumps and the processes with infinitely-active jump component. We use three different methods. First we use activity signature plots to estimate the activity patterns of jumps. Then we estimate the Blumenthal-Getoor index with Ait-Sahalia and Jacod threshold estimator.Then we use methods based on singularity spectra of Levy processes. Finally, we compare the results.