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Estimating the quadratic covariation matrix for asynchronously observed high frequency stock returns corrupted by additive measurement error

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  • Park, Sujin
  • Hong, Seok Young
  • Linton, Oliver

Abstract

This paper studies the estimation problem of the covariance matrices of asset returns in the presence of microstructure noise and asynchronicity between the observations across different assets. Motivated by Malliavin and Mancino (2002, 2009) we propose a new Fourier domain based estimator of multivariate ex-post volatility, which we call the Fourier Realized Kernel (FRK). An advantage of this approach is that no explicit time alignment is required unlike the time domain based methods widely adopted in the existing literature. We derive the large sample properties and establish asymptotic normality of our estimator under some general conditions that allow for both temporal and cross-sectional correlations in the measurement error process. Our results can be viewed as Frequency domain extension of the asymptotic theories for the multivariate realized kernel estimator of Barndorff-Nielsen et al. (2011). We show in extensive simulations that our method outperforms the time domain estimators when two assets with different liquidity are traded asynchronously.

Suggested Citation

  • Park, Sujin & Hong, Seok Young & Linton, Oliver, 2016. "Estimating the quadratic covariation matrix for asynchronously observed high frequency stock returns corrupted by additive measurement error," Journal of Econometrics, Elsevier, vol. 191(2), pages 325-347.
  • Handle: RePEc:eee:econom:v:191:y:2016:i:2:p:325-347
    DOI: 10.1016/j.jeconom.2015.12.005
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    References listed on IDEAS

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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    3. 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.
    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. Takaki Hayashi & Nakahiro Yoshida, 2008. "Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 367-406, June.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    7. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
    8. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    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. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    11. 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.
    12. Masayuki Hirukawa, 2006. "A Modified Nonparametric Prewhitened Covariance Estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 441-476, May.
    13. repec:hal:journl:peer-00732537 is not listed on IDEAS
    14. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    15. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
    16. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    17. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
    18. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
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    Cited by:

    1. Markus Bibinger & Per A. Mykland, 2016. "Inference for Multi-dimensional High-frequency Data with an Application to Conditional Independence Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1078-1102, December.

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