Asymptotic properties of realized power variations and related functionals of semimartingales
This paper is concerned with the asymptotic behavior of sums of the form , where X is a 1-dimensional semimartingale and f a suitable test function, typically f(x)=xr, as [Delta]n-->0. We prove a variety of "laws of large numbers", that is convergence in probability of Un(f)t, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.
Volume (Year): 118 (2008)
Issue (Month): 4 (April)
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References listed on IDEAS
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- Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006.
"Limit theorems for multipower variation in the presence of jumps,"
Stochastic Processes and their Applications,
Elsevier, vol. 116(5), pages 796-806, May.
- Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Papers 2005-W07, Economics Group, Nuffield College, University of Oxford.
- Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," OFRC Working Papers Series 2005fe06, Oxford Financial Research Centre.
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