Jumps Activity and Singularity Spectra for Instruments in the Polish Financial Market
DOI:
https://doi.org/10.12775/DEM.2011.012Keywords
Blumenthal-Getoor index, singularity spectrum, Lévy exponential modelsAbstract
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 Lévy 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 Aït-Sahalia and Jacod threshold estimator.Then we use methods based on singularity spectra of Lévy processes. Finally, we compare the results.
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