# Power Variation and Time Change

## Author Info

• Ole E. Barndorff-Nielsen

()
(University of Aarhus)

• Neil Shephard

()
(Nuffield College, University of Oxford)

Registered author(s):

## Abstract

This paper provides limit distribution results for power variation, that is sums of powers of absolute increments, for certain types of time-changed Brownian motion and $\alpha$-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial econometrics.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2002/w24/pvtc.pdf

## Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2002-W24.

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Length: 22 pages
Date of revision:
Handle: RePEc:nuf:econwp:0224

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Web page: http://www.nuff.ox.ac.uk/economics/

## Related research

Keywords: Power variation; r-variation; Realised variance; Semimartingales; Stochastic volatility; Time-change.;

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## References

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1. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Realised power variation and stochastic volatility models," Economics Series Working Papers 2001-W18, University of Oxford, Department of Economics.
2. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
3. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
4. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics," OFRC Working Papers Series 2002fe03, Oxford Financial Research Centre.
5. Ole E. Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2001. "Some recent developments in stochastic volatility modelling," Economics Papers 2001-W25, Economics Group, Nuffield College, University of Oxford.
6. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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## Citations

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Cited by:
1. Neil Shephard & Ole E. Barndorff-Nielsen, 2004. "Multipower Variation and Stochastic Volatility," Economics Series Working Papers 2004-FE-22, University of Oxford, Department of Economics.
2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," OFRC Working Papers Series 2004fe20, Oxford Financial Research Centre.
3. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
4. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Series Working Papers 2003-W18, University of Oxford, Department of Economics.
5. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007,23, Christian-Albrechts-University of Kiel, Department of Economics.
6. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.

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