Change points and uniform confidence for spot volatility

Madensoy, Mehmet

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URN: urn:nbn:de:bsz:180-madoc-541969
Document Type: Doctoral dissertation
Year of publication: 2020
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Bibinger, Markus
Date of oral examination: 17 January 2020
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
Subject: 510 Mathematics
Keywords (English): high-frequency , semimartingales , volatility , microstructure noise , change-points , uniform confidence
Abstract: We consider issues of high-frequency statistics, whereas our data is generated by discretization of noisy and pure Itô semimartingales. We present results and tools from stochastic calculus, high-frequency statistics and extreme value theory, being essential for all subsequent parts. Based on noisy Itô semimartingale observations, in the second part limit theorems are proved, which are necessary to tackle change-point questions in the volatility adequately. Furthermore, the consistency of a change-point test is proved as well as consistency of the associated change-point estimator. In the third and final part we prove weak limit theorems for extreme value statistics, which are appropriate for constructing uniform confidence bands for the volatility process. Those limit theorems include statistics, which are jump as well as noise robust.

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