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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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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    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.
    3. 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.
    4. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    5. Bibinger, Markus, 2012. "An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2411-2453.
    6. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    7. 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.
    8. repec:hal:journl:peer-00732537 is not listed on IDEAS
    9. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    10. Giuseppe Curci & Fulvio Corsi, 2012. "Discrete sine transform for multi-scale realized volatility measures§," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 263-279, April.
    11. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
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    Cited by:

    1. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2014. "Large Deviations Of The Realized (Co-)Volatility Vector," Working Papers hal-01082903, HAL.
    2. repec:eee:spapps:v:127:y:2017:i:9:p:2926-2960 is not listed on IDEAS
    3. 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.
    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. repec:eee:econom:v:208:y:2019:i:1:p:101-119 is not listed on IDEAS
    6. repec:kap:apfinm:v:24:y:2017:i:1:d:10.1007_s10690-017-9223-4 is not listed on IDEAS
    7. 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.
    8. Linzert, Tobias & Winkelmann, Lars & Bibinger, Markus, 2014. "ECB monetary policy surprises: identification through cojumps in interest rates," Working Paper Series 1674, European Central Bank.
    9. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.
    10. 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.
    11. 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.

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