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Understanding limit theorems for semimartingales: a short survey

  • Mark Podolskij


    (ETH Zürich and CREATES)

  • Mathias Vetter


    (Ruhr-University of Bochum)

This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We show some laws of large numbers (for the continuous and the discontinuous case) that are the most interesting from a practical point of view, and demonstrate the associated stable central limit theorems. Moreover, we state a simple sketch of the proofs and give some examples.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-47.

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Length: 21
Date of creation: 05 Oct 2009
Date of revision:
Handle: RePEc:aah:create:2009-47
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  1. 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.
  2. Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
  3. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278.
  4. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre.
  5. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  6. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
  7. Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Series Working Papers 2004-FE-21, University of Oxford, Department of Economics.
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