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Estimation of Quarticity with High Frequency Data

Author

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  • Maria Elvira Mancino

    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Simona Sanfelici

    (Dipartimento di Economia, Universita' di Parma)

Abstract

We propose a new methodology based on Fourier analysis to estimate the fourth power of volatility function (spot quarticity) and, as a byproduct, the integrated function. We prove consistency of the proposed estimator of integrated quarticity. Further we analyze its efficiency in the presence of microstructure noise, both from a theoretical and empirical viewpoint. Extensions to higher powers of volatility and to the multivariate case are also discussed.

Suggested Citation

  • Maria Elvira Mancino & Simona Sanfelici, 2011. "Estimation of Quarticity with High Frequency Data," Working Papers - Mathematical Economics 2011-06, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Jan 2012.
    • Handle: RePEc:flo:wpaper:2011-06
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Maria Elvira Mancino & Tommaso Mariotti & Giacomo Toscano, 2022. "Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise," Papers 2209.08967, arXiv.org.
    2. Recchioni, Maria Cristina & Tedeschi, Gabriele & Gallegati, Mauro, 2015. "A calibration procedure for analyzing stock price dynamics in an agent-based framework," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 1-25.
    3. Imma Valentina Curato, 2012. "Asymptotics for the Fourier estimators of the volatility of volatility and the leverage," Working Papers - Mathematical Economics 2012-11, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    4. Simon Clinet & Yoann Potiron, 2021. "Estimation for high-frequency data under parametric market microstructure noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 649-669, August.
    5. Clinet, Simon & Potiron, Yoann, 2018. "Efficient asymptotic variance reduction when estimating volatility in high frequency data," Journal of Econometrics, Elsevier, vol. 206(1), pages 103-142.
    6. Simona Sanfelici & Giacomo Toscano, 2024. "The Fourier-Malliavin Volatility (FMVol) MATLAB library," Papers 2402.00172, arXiv.org.
    7. Curato, Imma Valentina, 2019. "Estimation of the stochastic leverage effect using the Fourier transform method," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3207-3238.
    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.
    9. Imma Valentina Curato, 2013. "Fourier estimation of stochastic leverage using high frequency data," Working Papers - Mathematical Economics 2013-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    10. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.

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    Keywords

    volatility; covariance; quarticity; microstructure; Fourier analysis;
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