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Estimation of the characteristics of a Lévy process observed at arbitrary frequency

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  • Johanna Kappus
  • Markus Reiß

Abstract

A Lévy process is observed at time points of distance delta until time T. We construct an estimator of the Lévy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and delta. Thereby, we encompass the usual low- and high-frequency assumptions and obtain also asymptotics in the mid-frequency regime.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-015.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-015.

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Length: 18 pages
Date of creation: Feb 2010
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2010-015

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Keywords: Lévy process; Lévy-Khinchine characteristics; Nonparametric estimation; Inverse problem; Optimal rates of convergence;

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References

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  1. Mechtenberg, Lydia & Münster, Johannes, 2012. "A strategic mediator who is biased in the same direction as the expert can improve information transmission," Economics Letters, Elsevier, Elsevier, vol. 117(2), pages 490-492.
  2. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2010. "Unwillingness to pay for privacy: A field experiment," Discussion Papers, Research Unit: Market Behavior SP II 2010-03, Social Science Research Center Berlin (WZB).
  3. Dirk Hofmann & Salmai Qari, 2011. "The Law of Attraction: Bilateral Search and Horizontal Heterogeneity," SFB 649 Discussion Papers SFB649DP2011-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Wolfgang Karl Härdle & Brenda López Cabrera & Ostap Okhrin & Weining Wang, 2011. "Localising temperature risk," SFB 649 Discussion Papers SFB649DP2011-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Rong Liu & Lijian Yang & Wolfgang Karl Härdle, 2011. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," SFB 649 Discussion Papers SFB649DP2011-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Till Strohsal & Enzo Weber, 2011. "Mean-Variance Cointegration and the Expectations Hypothesis," SFB 649 Discussion Papers SFB649DP2011-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Alexander Meyer-Gohde, 2011. "Sticky Information and Determinacy," SFB 649 Discussion Papers SFB649DP2011-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Juliane Scheffel, 2011. "How do Unusual Working Schedules Affect Social Life?," SFB 649 Discussion Papers SFB649DP2011-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Wolfgang Karl Hardle and Maria Osipenko, 2012. "Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity," The Energy Journal, International Association for Energy Economics, International Association for Energy Economics, vol. 0(Number 2).
  10. Esra Akdeniz Duran & Mengmeng Guo & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Expectile Functions," SFB 649 Discussion Papers SFB649DP2011-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 105(1), pages 164-175.
  12. Xiaoliang Liu & Wei Xu & Martin Odening, 2011. "Can crop yield risk be globally diversified?," SFB 649 Discussion Papers SFB649DP2011-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  13. Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  14. Lu Lin & Feng Li & Lixing Zhu & Wolfgang Karl Härdle, 2011. "Mean Volatility Regressions," SFB 649 Discussion Papers SFB649DP2011-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  15. Juliane Scheffel, 2011. "Identifying the Effect of Temporal Work Flexibility on Parental Time with Children," SFB 649 Discussion Papers SFB649DP2011-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  16. Wolfgang Karl Härdle & Vladimir Spokoiny & Weining Wang, 2011. "Local Quantile Regression," SFB 649 Discussion Papers SFB649DP2011-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2010-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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