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The speed of convergence of the Threshold estimator of integrated variance

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  • Mancini, Cecilia

Abstract

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the Threshold estimator is able to separate the integrated variance IV from the sum of the squared jumps. This has importance in measuring and forecasting the asset risks. In this paper we provide the exact speed of convergence of , a result which was known in the literature only in the case of jumps with finite variation. This has practical relevance since many models used have jumps of infinite variation (see e.g. Carr et al. (2002) [4]).

Suggested Citation

  • Mancini, Cecilia, 2011. "The speed of convergence of the Threshold estimator of integrated variance," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 845-855, April.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:845-855
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    References listed on IDEAS

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    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. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    3. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, July.
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    Cited by:

    1. Arnaud Gloter & Dasha Loukianova & Hilmar Mai, 2016. "Jump filtering and efficient drift estimation for Lévy-Driven SDE’S," Working Papers 2016-04, Center for Research in Economics and Statistics.
    2. Yuan Gao & Honglong You, 2021. "The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α -Stable Lévy Subordinator," Mathematics, MDPI, vol. 9(21), pages 1-9, October.
    3. 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.
    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. Mancini, Cecilia, 2017. "Truncated Realized Covariance when prices have infinite variation jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1998-2035.
    6. Amorino, Chiara & Gloter, Arnaud, 2020. "Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5888-5939.
    7. B. Cooper Boniece & Jos'e E. Figueroa-L'opez & Yuchen Han, 2023. "Data-driven fixed-point tuning for truncated realized variations," Papers 2311.00905, arXiv.org, revised Oct 2024.
    8. Figueroa-López, José E. & Mancini, Cecilia, 2019. "Optimum thresholding using mean and conditional mean squared error," Journal of Econometrics, Elsevier, vol. 208(1), pages 179-210.
    9. Cheng, Mingmian & Liao, Yuan & Yang, Xiye, 2023. "Uniform predictive inference for factor models with instrumental and idiosyncratic betas," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Mancini, Cecilia, 2013. "Measuring the relevance of the microstructure noise in financial data," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2728-2751.
    11. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.

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