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

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

Till Sabel

Doctoral thesis

Date of Examination: 2014-07-16

Date of issue: 2014-07-28

Advisor: Munk, Axel Prof. Dr.

Referee: Munk, Axel Prof. Dr.

Referee: Dümbgen, Lutz Prof. Dr.

Persistent Address: http://hdl.handle.net/11858/00-1735-0000-0022-5F35-2

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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