IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i8p2699-2753.html
   My bibliography  Save this article

Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

Author

Listed:
  • Koike, Yuta

Abstract

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.

Suggested Citation

  • Koike, Yuta, 2014. "Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2699-2753.
  • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2699-2753
    DOI: 10.1016/j.spa.2014.03.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914000672
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. 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.
    3. Hayashi, Takaki & Yoshida, Nakahiro, 2011. "Nonsynchronous covariation process and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2416-2454, October.
    4. 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.
    5. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    6. 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.
    7. 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.
    8. 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.
    9. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    10. Fukasawa, Masaaki, 2010. "Realized volatility with stochastic sampling," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 829-852, June.
    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. Rasmus Tangsgaard Varneskov, 2011. "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices," CREATES Research Papers 2011-35, Department of Economics and Business Economics, Aarhus University.
    13. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    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. Christensen, Kim & Podolskij, Mark & Vetter, Mathias, 2013. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 59-84.
    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. 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.
    18. Takaki Hayashi & Shigeo Kusuoka, 2008. "Consistent estimation of covariation under nonsynchronicity," Statistical Inference for Stochastic Processes, Springer, vol. 11(1), pages 93-106, February.
    19. Clément, Emmanuelle & Gloter, Arnaud, 2011. "Limit theorems in the Fourier transform method for the estimation of multivariate volatility," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1097-1124, May.
    20. repec:hal:journl:peer-00732537 is not listed on IDEAS
    21. Michael C. Munnix & Rudi Schafer & Thomas Guhr, 2010. "Impact of the tick-size on financial returns and correlations," Papers 1001.5124, arXiv.org, revised Jul 2010.
    22. Münnix, Michael C. & Schäfer, Rudi & Guhr, Thomas, 2010. "Impact of the tick-size on financial returns and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4828-4843.
    23. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Potiron, Yoann & Mykland, Per A., 2017. "Estimation of integrated quadratic covariation with endogenous sampling times," Journal of Econometrics, Elsevier, vol. 197(1), pages 20-41.
    2. Zhi Liu, 2016. "Estimating integrated co-volatility with partially miss-ordered high frequency data," Statistical Inference for Stochastic Processes, Springer, vol. 19(2), pages 175-197, July.
    3. 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.
    4. 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.
    5. Yuta Koike, 2017. "Time endogeneity and an optimal weight function in pre-averaging covariance estimation," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 15-56, April.
    6. Ikeda, Shin S., 2016. "A bias-corrected estimator of the covariation matrix of multiple security prices when both microstructure effects and sampling durations are persistent and endogenous," Journal of Econometrics, Elsevier, vol. 193(1), pages 203-214.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2699-2753. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.