Simultaneous Confidence Statements about the Diffusion Coefficient of an Ito-Process with Application to Spot Volatility Estimation
von Till Sabel
Datum der mündl. Prüfung:2014-07-16
Erschienen:2014-07-28
Betreuer:Prof. Dr. Axel Munk
Gutachter:Prof. Dr. Axel Munk
Gutachter:Prof. Dr. Lutz Dümbgen
Dateien
Name:sabel_diss.pdf
Size:979.Kb
Format:PDF
Zusammenfassung
Englisch
In this PhD thesis, we address the problem of giving simultaneous confidence statements about local features of the diffusion of an Itô process. To this end, we construct a multiscale test based on weighted quadratic variation and prove that the test statistic can be strongly approximated by a sequence of Gaussian martingales which are distribution-free. Further, we give optimality results and present different visualization methods. In the second part of the thesis, we extend the approach to data corrupted by additive noise to cover applications from high-frequency finance. Additionally, we show which difficulties arise from real data and apply our method exemplarily to prices of Euro-Bund-Futures (FGBL). As an outlook for future work, we present ideas of generalizing the method to inference on the local covariance and point out some interesting applications from finance.
Keywords: nonparametric statistics; multiscale testing; volatility estimation