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A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data

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  • Liu, Cheng
  • Tang, Cheng Yong

Abstract

Estimating the integrated covariance matrix (ICM) from high frequency financial trading data is crucial to reflect the volatilities and covariations of the underlying trading instruments. Such an objective is difficult due to contaminated data with microstructure noises, asynchronous trading records, and increasing data dimensionality. In this paper, we study a quasi-maximum likelihood (QML) approach for estimating an ICM from high frequency financial data. We explore a novel multivariate moving average time series device that is convenient for evaluating the estimator both theoretically for its asymptotic properties and numerically for its practical implementations. We demonstrate that the QML estimator is consistent to the ICM, and is asymptotically normally distributed. Efficiency gain of the QML approach is theoretically quantified, and numerically demonstrated via extensive simulation studies. An application of the QML approach is illustrated through analyzing a high frequency financial trading data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:180:y:2014:i:2:p:217-232
    DOI: 10.1016/j.jeconom.2014.01.008
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    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. 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.
    3. Chang, Jinyuan & Hu, Qiao & Liu, Cheng & Tang, Cheng Yong, 2024. "Optimal covariance matrix estimation for high-dimensional noise in high-frequency data," Journal of Econometrics, Elsevier, vol. 239(2).
    4. 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.
    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. Michael Ho & Jack Xin, 2016. "Sparse Kalman Filtering Approaches to Covariance Estimation from High Frequency Data in the Presence of Jumps," Papers 1602.02185, arXiv.org, revised Apr 2016.
    7. Ulrich Hounyo, 2014. "Bootstrapping integrated covariance matrix estimators in noisy jump-diffusion models with non-synchronous trading," CREATES Research Papers 2014-35, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    High frequency data; Integrated covariance matrix; Microstructure noises; Quasi-maximum likelihood;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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