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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.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf05.

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Date of creation: 2002
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Handle: RePEc:sbs:wpsefe:2002mf05

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  3. 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. [Downloadable!] (restricted)
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  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  9. John W. Galbraith & Victoria Zinde-Walsh, 2000. "Properties of Estimates of Daily GARCH Parameters Based on Intra-Day Observations," Econometric Society World Congress 2000 Contributed Papers 1800, Econometric Society. [Downloadable!]
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  12. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO. [Downloadable!]
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  13. Fulvio Corsi & Gilles Zumbach & Ulrich Müller & Michel Dacorogna, 2004. "Consistent high-precision volatility from high-frequency data," Finance 0407005, EconWPA. [Downloadable!]
  14. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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  16. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June. [Downloadable!] (restricted)
  17. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
  2. Elena Andreou & Eric Ghysels, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," CIRANO Working Papers 2004s-25, CIRANO. [Downloadable!]
  3. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," NBER Working Papers 10914, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
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