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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