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Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps

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  • Hacène Djellout

    (Université Blaise Pascal)

  • Hui Jiang

    (Nanjing University of Aeronautics and Astronautics)

Abstract

Recently considerable interest has been paid to the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this paper, we adopt the threshold estimator introduced by Mancini (Scand Actuar J 1:42–52, 2004) where only the variations under a given threshold function are taken into account. The purpose of this work is to investigate large and moderate deviations for the threshold estimator of the integrated variance–covariance vector. This paper is an extension of the previous work in Djellout et al. (Stoch Process Appl 1–35, 2017), where the problem has been studied in the absence of a jump component. We will use the approximation lemma to prove large and moderate deviations results. As the reader can expect, we obtain the same results as in the case without jump.

Suggested Citation

  • Hacène Djellout & Hui Jiang, 2018. "Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1606-1624, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0759-z
    DOI: 10.1007/s10959-017-0759-z
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    References listed on IDEAS

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    1. Shimizu, Yasutaka, 2009. "Functional estimation for Lvy measures of semimartingales with Poissonian jumps," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1073-1092, July.
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    4. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.
    5. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
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    7. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    8. Hacène Djellout & Arnaud Guillin & Liming Wu, 1999. "Large and Moderate Deviations for Estimators of Quadratic Variational Processes of Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 2(3), pages 195-225, October.
    9. Mancini, Cecilia, 2008. "Large deviation principle for an estimator of the diffusion coefficient in a jump-diffusion process," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 869-879, May.
    10. 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.
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    13. Djellout, Hacène & Samoura, Yacouba, 2014. "Large and moderate deviations of realized covolatility," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 30-37.
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