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On critical cases in limit theory for stationary increments Lévy driven moving averages

Author

Listed:
  • Andreas Basse-O'Connor

    (Department of Mathematics)

  • Mark Podolskij

    (Department of Mathematics and CREATES)

Abstract

In this paper we present some limit theorems for power variation of stationary increments Lévy driven moving averages in the setting of critical regimes. In [5] the authors derived first and second order asymptotic results for k-th order increments of stationary increments Lévy driven moving averages. The limit theory heavily depends on the interplay between the given order of the increments, the considered power, the Blumenthal-Getoor index of the driving pure jump Lévy process L and the behavior of the kernel function g at 0. In this work we will study the critical cases, which were not covered in the original work [5].

Suggested Citation

  • Andreas Basse-O'Connor & Mark Podolskij, 2015. "On critical cases in limit theory for stationary increments Lévy driven moving averages," CREATES Research Papers 2015-57, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-57
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    File URL: https://repec.econ.au.dk/repec/creates/rp/15/rp15_57.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Cambanis, Stamatis & Hardin, Clyde D. & Weron, Aleksander, 1987. "Ergodic properties of stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 1-18, February.
    3. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 329-351, August.
    4. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    5. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
    6. Andreas Basse-O'Connor & Raphaël Lachièze-Rey & Mark Podolskij, 2015. "Limit theorems for stationary increments Lévy driven moving averages," CREATES Research Papers 2015-56, Department of Economics and Business Economics, Aarhus University.
    7. Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Mark Podolskij & Nopporn Thamrongrat, 2015. "A weak limit theorem for numerical approximation of Brownian semi-stationary processes," CREATES Research Papers 2015-53, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Power variation; limit theorems; moving averages; fractional processes; stable convergence; high frequency data;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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