Simultaneous Confidence Statements about the Diffusion Coefficient of an Ito-Process with Application to Spot Volatility Estimation

by Till Sabel
Doctoral thesis
Date of Examination:2014-07-16
Date of issue:2014-07-28
Advisor:Prof. Dr. Axel Munk
Referee:Prof. Dr. Axel Munk
Referee:Prof. Dr. Lutz Dümbgen
Persistent Address: http://dx.doi.org/10.53846/goediss-4610

 

 

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Abstract

English

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
 
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