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Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

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  • Markus Bibinger
  • Markus Reiß

Abstract

type="main" xml:id="sjos12019-abs-0001"> We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time-varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white-noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous-time and discrete-time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non-parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.

Suggested Citation

  • Markus Bibinger & Markus Reiß, 2014. "Spectral Estimation of Covolatility from Noisy Observations Using Local Weights," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 23-50, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:23-50
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    File URL: http://hdl.handle.net/10.1111/sjos.12019
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    References listed on IDEAS

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    2. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
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    5. Markus Bibinger, 2011. "Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 23-45, March.
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    8. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    9. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
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    Cited by:

    1. Mustafayeva, Konul & Wang, Weining, 2020. "Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data," IRTG 1792 Discussion Papers 2020-025, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. 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.
    3. Naoto Kunitomo & Daisuke Kurisu, 2017. "Effects of Jumps and Small Noise in High-Frequency Financial Econometrics," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 39-73, March.
    4. Boudt, Kris & Laurent, Sébastien & Lunde, Asger & Quaedvlieg, Rogier & Sauri, Orimar, 2017. "Positive semidefinite integrated covariance estimation, factorizations and asynchronicity," Journal of Econometrics, Elsevier, vol. 196(2), pages 347-367.
    5. 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.
    6. Bibinger, Markus & Winkelmann, Lars, 2015. "Econometrics of co-jumps in high-frequency data with noise," Journal of Econometrics, Elsevier, vol. 184(2), pages 361-378.
    7. Torben G. Andersen & Martin Thyrsgaard & Viktor Todorov, 2021. "Recalcitrant betas: Intraday variation in the cross‐sectional dispersion of systematic risk," Quantitative Economics, Econometric Society, vol. 12(2), pages 647-682, May.
    8. Mykland, Per A. & Zhang, Lan & Chen, Dachuan, 2019. "The algebra of two scales estimation, and the S-TSRV: High frequency estimation that is robust to sampling times," Journal of Econometrics, Elsevier, vol. 208(1), pages 101-119.
    9. Seisho Sato & Naoto Kunitomo, 2015. "A Robust Estimation of Integrated Volatility under Round-off Errors, Micro-market Price Adjustments and Noises," CIRJE F-Series CIRJE-F-964, CIRJE, Faculty of Economics, University of Tokyo.
    10. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2014. "Large Deviations Of The Realized (Co-)Volatility Vector," Working Papers hal-01082903, HAL.
    11. 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.
    12. Linzert, Tobias & Winkelmann, Lars & Bibinger, Markus, 2014. "ECB monetary policy surprises: identification through cojumps in interest rates," Working Paper Series 1674, European Central Bank.
    13. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.

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