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On the class of distributions of subordinated Lévy processes and bases

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  • Sauri, Orimar
  • Veraart, Almut E.D.

Abstract

This article studies the class of distributions obtained by subordinating Lévy processes and Lévy bases by independent subordinators and meta-times. To do this we derive properties of a suitable mapping obtained via Lévy mixing. We show that our results can be used to solve the so-called recovery problem for general Lévy bases as well as for moving average processes which are driven by subordinated Lévy processes.

Suggested Citation

  • Sauri, Orimar & Veraart, Almut E.D., 2017. "On the class of distributions of subordinated Lévy processes and bases," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 475-496.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:2:p:475-496
    DOI: 10.1016/j.spa.2016.06.015
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    References listed on IDEAS

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    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Marc Yor & Dilip B. Madan & Hélyette Geman, 2002. "Stochastic volatility, jumps and hidden time changes," Finance and Stochastics, Springer, vol. 6(1), pages 63-90.
    3. Almut E. D. Veraart & Luitgard A. M. Veraart, 2012. "Modelling electricity day–ahead prices by multivariate Lévy semistationary processes," CREATES Research Papers 2012-13, Department of Economics and Business Economics, Aarhus University.
    4. Rosinski, Jan, 1989. "On path properties of certain infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 73-87, October.
    5. Corcuera, José Manuel & Hedevang, Emil & Pakkanen, Mikko S. & Podolskij, Mark, 2013. "Asymptotic theory for Brownian semi-stationary processes with application to turbulence," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2552-2574.
    6. Adler, R. J. & Monrad, D. & Scissors, R. H. & Wilson, R., 1983. "Representations, decompositions and sample function continuity of random fields with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 3-30, June.
    7. Comte, F. & Renault, E., 1996. "Noncausality in Continuous Time Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 215-256, June.
    8. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    9. Peter J. Brockwell & Vincenzo Ferrazzano & Claudia Klüppelberg, 2013. "High-frequency sampling and kernel estimation for continuous-time moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 385-404, May.
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    Cited by:

    1. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.

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