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Positive semidefinite integrated covariance estimation, factorizations and asynchronicity

Author

Listed:
  • Kris Boudt

    (VUB - Vrije Universiteit Brussel)

  • Sébastien Laurent

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Asger Lunde

    (Aarhus University [Aarhus])

  • Rogier Quaedvlieg

    (Maastricht University [Maastricht])

  • Orimar Sauri

    (Aarhus University [Aarhus])

Abstract

An estimator of the ex-post covariation of log-prices under asynchronicity and microstructure noise is proposed. It uses the Cholesky factorization of the covariance matrix in order to exploit the heterogeneity in trading intensities to estimate the different parameters sequentially with as many observations as possible. The estimator is positive semidefinite by construction. We derive asymptotic results and confirm their good finite sample properties by means of a Monte Carlo simulation. In the application we forecast portfolio Value-at-Risk and sector risk exposures for a portfolio of 52 stocks. We find that the dynamic models utilizing the proposed high-frequency estimator provide statistically and economically superior forecasts.

Suggested Citation

  • Kris Boudt & Sébastien Laurent & Asger Lunde & Rogier Quaedvlieg & Orimar Sauri, 2017. "Positive semidefinite integrated covariance estimation, factorizations and asynchronicity," Post-Print hal-01505775, HAL.
    • Handle: RePEc:hal:journl:hal-01505775
    DOI: 10.1016/j.jeconom.2016.09.016
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01505775
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    Cited by:

    1. Boudt, Kris & Dragun, Kirill & Sauri, Orimar & Vanduffel, Steven, 2023. "ETF Basket-Adjusted Covariance estimation," Journal of Econometrics, Elsevier, vol. 235(2), pages 1144-1171.
    2. Bauwens, Luc & Braione, Manuela & Storti, Giuseppe, 2017. "A dynamic component model for forecasting high-dimensional realized covariance matrices," Econometrics and Statistics, Elsevier, vol. 1(C), pages 40-61.
    3. Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    4. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," LIDAM Discussion Papers CORE 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Opschoor, Anne & van Dijk, Dick & van der Wel, Michel, 2014. "Predicting volatility and correlations with Financial Conditions Indexes," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 435-447.
    6. Nabil Bouamara & Kris Boudt & S'ebastien Laurent & Christopher J. Neely, 2023. "Sluggish news reactions: A combinatorial approach for synchronizing stock jumps," Papers 2309.15705, arXiv.org.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    8. Kirill Dragun & Kris Boudt & Orimar Sauri & Steven Vanduffel, 2021. "Beta-Adjusted Covariance Estimation," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 21/1010, Ghent University, Faculty of Economics and Business Administration.
    9. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    10. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    11. Jean-Claude Hessing & Rutger-Jan Lange & Daniel Ralph, 2022. "This article establishes the Poisson optional stopping times (POST) method by Lange et al. (2020) as a near-universal method for solving liquidity-constrained American options, or, equivalently, penal," Tinbergen Institute Discussion Papers 22-007/IV, Tinbergen Institute.
    12. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.

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    More about this item

    Keywords

    Reali; Cholesky decomposition; Integrated covariance; Non-synchronous trading; Positive semidefinite;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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