IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v203y2018i1p69-79.html
   My bibliography  Save this article

Adaptive thresholding for large volatility matrix estimation based on high-frequency financial data

Author

Listed:
  • Kim, Donggyu
  • Kong, Xin-Bing
  • Li, Cui-Xia
  • Wang, Yazhen

Abstract

Universal thresholding methods have been developed to estimate the large sparse integrated volatility matrix of underlying assets based on high-frequency financial data. Since the integrated volatility matrix often has entries with a wide range of variability, universal thresholding estimators do not take the varying entries into consideration and may have unsatisfactory performances. This paper investigates adaptive thresholding estimation of the large integrated volatility matrix. We first construct an estimator for the asymptotic variance of the pre-averaging realized volatility estimator and then use the two estimators to develop an adaptive thresholding estimator of the large volatility matrix. It is shown that the adaptive thresholding estimator can achieve the optimal rate of convergence over the class of the sparse integrated volatility matrix when both the number of assets and sample size are allowed to go to infinity, while the universal thresholding estimator can achieve only the sub-optimal convergence rate. Also we discuss how to harness the adaptive thresholding scheme in the approximate factor model. The simulation study is conducted to check the finite sample performance of the adaptive thresholding estimators.

Suggested Citation

  • Kim, Donggyu & Kong, Xin-Bing & Li, Cui-Xia & Wang, Yazhen, 2018. "Adaptive thresholding for large volatility matrix estimation based on high-frequency financial data," Journal of Econometrics, Elsevier, vol. 203(1), pages 69-79.
    • Handle: RePEc:eee:econom:v:203:y:2018:i:1:p:69-79
    DOI: 10.1016/j.jeconom.2017.09.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407617302270
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2017.09.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. 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.
    4. 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.
    5. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    6. 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.
    7. 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.
    8. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    9. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    10. Tao, Minjing & Wang, Yazhen & Chen, Xiaohong, 2013. "Fast Convergence Rates In Estimating Large Volatility Matrices Using High-Frequency Financial Data," Econometric Theory, Cambridge University Press, vol. 29(4), pages 838-856, August.
    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. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    13. Ole E. Barndorff‐Nielsen & Neil 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, May.
    14. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    15. Kim, Donggyu & Wang, Yazhen & Zou, Jian, 2016. "Asymptotic theory for large volatility matrix estimation based on high-frequency financial data," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3527-3577.
    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. Kim, Donggyu & Wang, Yazhen, 2016. "Sparse PCA-based on high-dimensional Itô processes with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 172-189.
    18. Xin-Bing Kong, 2017. "On the number of common factors with high-frequency data," Biometrika, Biometrika Trust, vol. 104(2), pages 397-410.
    19. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    20. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    21. Jianqing Fan & Alex Furger & Dacheng Xiu, 2016. "Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 489-503, October.
    22. repec:hal:journl:peer-00732537 is not listed on IDEAS
    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. Kong, Xin-Bing & Liu, Zhi & Zhou, Wang, 2019. "A rank test for the number of factors with high-frequency data," Journal of Econometrics, Elsevier, vol. 211(2), pages 439-460.
    2. Jiayuan Zhou & Feiyu Jiang & Ke Zhu & Wai Keung Li, 2019. "Time series models for realized covariance matrices based on the matrix-F distribution," Papers 1903.12077, arXiv.org, revised Jul 2020.
    3. Erlin Guo & Cuixia Li & Fengqin Tang, 2023. "The Convergence Rates of Large Volatility Matrix Estimator Based on Noise, Jumps, and Asynchronization," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    4. Choi, Sung Hoon & Kim, Donggyu, 2023. "Large volatility matrix analysis using global and national factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1917-1933.
    5. Donggyu Kim & Minseog Oh, 2023. "Dynamic Realized Minimum Variance Portfolio Models," Papers 2310.13511, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fan, Jianqing & Kim, Donggyu, 2019. "Structured volatility matrix estimation for non-synchronized high-frequency financial data," Journal of Econometrics, Elsevier, vol. 209(1), pages 61-78.
    2. Kim, Donggyu & Fan, Jianqing, 2019. "Factor GARCH-Itô models for high-frequency data with application to large volatility matrix prediction," Journal of Econometrics, Elsevier, vol. 208(2), pages 395-417.
    3. Kim, Donggyu & Song, Xinyu & Wang, Yazhen, 2022. "Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    4. Kim, Donggyu & Wang, Yazhen & Zou, Jian, 2016. "Asymptotic theory for large volatility matrix estimation based on high-frequency financial data," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3527-3577.
    5. Donggyu Kim & Xinyu Song & Yazhen Wang, 2020. "Unified Discrete-Time Factor Stochastic Volatility and Continuous-Time Ito Models for Combining Inference Based on Low-Frequency and High-Frequency," Papers 2006.12039, arXiv.org.
    6. Bu, R. & Li, D. & Linton, O. & Wang, H., 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Janeway Institute Working Papers 2208, Faculty of Economics, University of Cambridge.
    7. Donggyu Kim & Minseog Oh, 2023. "Dynamic Realized Minimum Variance Portfolio Models," Papers 2310.13511, arXiv.org.
    8. Ruijun Bu & Degui Li & Oliver Linton & Hanchao Wang, 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Working Papers 202212, University of Liverpool, Department of Economics.
    9. Dai, Chaoxing & Lu, Kun & Xiu, Dacheng, 2019. "Knowing factors or factor loadings, or neither? Evaluating estimators of large covariance matrices with noisy and asynchronous data," Journal of Econometrics, Elsevier, vol. 208(1), pages 43-79.
    10. Shephard, Neil & Xiu, Dacheng, 2017. "Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading," Journal of Econometrics, Elsevier, vol. 201(1), pages 19-42.
    11. Xinyu Song, 2019. "Large Volatility Matrix Prediction with High-Frequency Data," Papers 1907.01196, arXiv.org, revised Sep 2019.
    12. Kim, Donggyu & Wang, Yazhen, 2016. "Sparse PCA-based on high-dimensional Itô processes with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 172-189.
    13. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    14. Song, Xinyu & Kim, Donggyu & Yuan, Huiling & Cui, Xiangyu & Lu, Zhiping & Zhou, Yong & Wang, Yazhen, 2021. "Volatility analysis with realized GARCH-Itô models," Journal of Econometrics, Elsevier, vol. 222(1), pages 393-410.
    15. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    16. Lam, Clifford & Feng, Phoenix, 2018. "A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data," Journal of Econometrics, Elsevier, vol. 206(1), pages 226-257.
    17. Liu, Cheng & Tang, Cheng Yong, 2014. "A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data," Journal of Econometrics, Elsevier, vol. 180(2), pages 217-232.
    18. Liu, Zhi & Kong, Xin-Bing & Jing, Bing-Yi, 2018. "Estimating the integrated volatility using high-frequency data with zero durations," Journal of Econometrics, Elsevier, vol. 204(1), pages 18-32.
    19. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.
    20. Cai, T. Tony & Hu, Jianchang & Li, Yingying & Zheng, Xinghua, 2020. "High-dimensional minimum variance portfolio estimation based on high-frequency data," Journal of Econometrics, Elsevier, vol. 214(2), pages 482-494.

    More about this item

    Keywords

    Pre-averaging realized volatility; Regularization; Sparsity; Adaptive thresholding; Diffusion; Integrated volatility;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

    Statistics

    Access and download statistics

    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:econom:v:203:y:2018:i:1:p:69-79. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.