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An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility

Author

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  • Clément, Emmanuelle
  • Delattre, Sylvain
  • Gloter, Arnaud

Abstract

This paper proposes a general approach to obtain asymptotic lower bounds for the estimation of random functionals. The main result is an abstract convolution theorem in a non parametric setting, based on an associated LAMN property. This result is then applied to the estimation of the integrated volatility, or related quantities, of a diffusion process, when the diffusion coefficient depends on an independent Brownian motion.

Suggested Citation

  • Clément, Emmanuelle & Delattre, Sylvain & Gloter, Arnaud, 2013. "An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2500-2521.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:7:p:2500-2521
    DOI: 10.1016/j.spa.2013.04.004
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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. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
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    Cited by:

    1. repec:hum:wpaper:sfb649dp2014-005 is not listed on IDEAS
    2. Altmeyer, Randolf & Bibinger, Markus, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers 2014-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Yang, Xiye, 2020. "Time-invariant restrictions of volatility functionals: Efficient estimation and specification tests," Journal of Econometrics, Elsevier, vol. 215(2), pages 486-516.
    4. Jean Jacod, 2019. "Estimation of volatility in a high-frequency setting: a short review," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 351-385, December.
    5. Li, Jia & Todorov, Viktor & Tauchen, George, 2017. "Adaptive estimation of continuous-time regression models using high-frequency data," Journal of Econometrics, Elsevier, vol. 200(1), pages 36-47.
    6. Altmeyer, Randolf & Bibinger, Markus, 2015. "Functional stable limit theorems for quasi-efficient spectral covolatility estimators," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4556-4600.
    7. Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    8. Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2019. "Asymptotic results for the Fourier estimator of the integrated quarticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 471-502, December.

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