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Variational Sums and Power Variation: a unifying approach to model selection and estimation in semimartingale models

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  • Jeannette H.C. Woerner

Abstract

In the framework of general semimartingale models we provide limit theorems for variational sums including the p-th power variation, i.e. the sum of p-th absolute powers of increments of a process. This gives new insight in the use of quadratic and realised power variation as an estimate for the integrated volatility in finance. It also provides a criterion to decide from high frequency data, whether a jump component should be included in the model. Furthermore, results on the asymptotic behaviour of integrals with respect to Levy processes, estimates for integrals with respect to Levy measures and non-parametric estimation for Levy processes will be derived and viewed in the framework of variational sums.

Suggested Citation

  • Jeannette H.C. Woerner, 2002. "Variational Sums and Power Variation: a unifying approach to model selection and estimation in semimartingale models," OFRC Working Papers Series 2002mf05, Oxford Financial Research Centre.
    • Handle: RePEc:sbs:wpsefe:2002mf05
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2002mf05.pdf
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    Cited by:

    1. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    2. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Power variation and stochastic volatility: a review and some new results," Economics Series Working Papers 2003-W19, University of Oxford, Department of Economics.
    3. Ole E. Barndorff-Nielsen & Svend Erik Graversen & Neil Shephard, 2003. "Power variation & stochastic volatility: a review and some new results," Economics Papers 2003-W19, Economics Group, Nuffield College, University of Oxford.
    4. Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 290-318.
    5. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.

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