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Fast Convergence Rates In Estimating Large Volatility Matrices Using High-Frequency Financial Data

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  • Tao, Minjing
  • Wang, Yazhen
  • Chen, Xiaohong

Abstract

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the number of assets and the sample size go to infinity, we show that our new estimator is consistent and achieves a fast convergence rate, where the rate is optimal with respect to the sample size. A simulation study is conducted to check the finite sample performance of the proposed estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:838-856_00
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    Citations

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    Cited by:

    1. 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).
    2. Minseog Oh & Donggyu Kim, 2024. "Effect of the U.S.–China Trade War on Stock Markets: A Financial Contagion Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 22(4), pages 954-1005.
    3. 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.
    4. 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.
    5. 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.
    6. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    7. Dohyun Chun & Donggyu Kim, 2022. "State Heterogeneity Analysis of Financial Volatility using high‐frequency Financial Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 105-124, January.
    8. 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.
    9. Kim, Donggyu & Wang, Yazhen, 2016. "Unified discrete-time and continuous-time models and statistical inferences for merged low-frequency and high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 220-230.
    10. Donggyu Kim & Minseok Shin & Yazhen Wang, 2023. "Overnight GARCH-Itô Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1215-1227, October.
    11. 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.
    12. Lam, Clifford & Feng, Phoenix, 2018. "A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data," LSE Research Online Documents on Economics 88375, London School of Economics and Political Science, LSE Library.
    13. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    14. 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.
    15. Donggyu Kim, 2016. "Statistical Inference for Unified Garch–Itô Models with High-Frequency Financial Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 513-532, July.
    16. Li, Y-N. & Chen, J. & Linton, O., 2021. "Estimation of Common Factors for Microstructure Noise and Efficient Price in a High-frequency Dual Factor Model," Cambridge Working Papers in Economics 2150, Faculty of Economics, University of Cambridge.
    17. Xinyu Song, 2019. "Large Volatility Matrix Prediction with High-Frequency Data," Papers 1907.01196, arXiv.org, revised Sep 2019.
    18. 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.
    19. 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.
    20. 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.
    21. Esparcia, Carlos & López, Raquel, 2024. "Performance of crypto-Forex portfolios based on intraday data," Research in International Business and Finance, Elsevier, vol. 69(C).
    22. Sung Hoon Choi & Donggyu Kim, 2024. "Cubic-based Prediction Approach for Large Volatility Matrix using High-Frequency Financial Data," Papers 2412.04293, arXiv.org.

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