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Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity

Author

Listed:
  • Kris Boudt

    (Department of Business, Vrije Universiteit Brussel, Belgium and VU University Amsterdam, Netherlands)

  • Sébastien Laurent

    (Aix-Marseille University, Aix-Marseille School of Economics, CNRS & EHESS, France)

  • Asger Lunde

    (Aarhus University and CREATES)

  • Rogier Quaedvlieg

    (Department of Finance, Maastricht University, Netherlands)

Abstract

An estimator of the ex-post covariation of log-prices under asynchronicity and microstructure noise is proposed. It uses the Cholesky factorization on the correlation matrix in order to exploit the heterogeneity in trading intensity to estimate the different parameters sequentially with as many observations as possible. The estimator is guaranteed positive semidefinite. Monte Carlo simulations confirm good finite sample properties. In the application we forecast portfolio Value-at-Risk and sector risk exposures for a portfolio of 52 stocks. We find that forecasts obtained from dynamic models utilizing the proposed high-frequency estimator provide statistically and economically superior forecasts to models using daily returns.

Suggested Citation

  • Kris Boudt & Sébastien Laurent & Asger Lunde & Rogier Quaedvlieg, 2014. "Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity," CREATES Research Papers 2014-05, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-05
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Cai, Zhanrui & Li, Changcheng & Wen, Jiawei & Yang, Songshan, 2024. "Asset splitting algorithm for ultrahigh dimensional portfolio selection and its theoretical property," Journal of Econometrics, Elsevier, vol. 239(2).
    6. Boudt, Kris & Dragun, Kirill & Sauri, Orimar & Vanduffel, Steven, 2023. "ETF Basket-Adjusted Covariance estimation," Journal of Econometrics, Elsevier, vol. 235(2), pages 1144-1171.
    7. 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.
    8. 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.
    9. 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.
    10. Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    11. 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).
    12. D’Innocenzo, Enzo & Lucas, Andre, 2024. "Dynamic partial correlation models," Journal of Econometrics, Elsevier, vol. 241(2).
    13. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    14. 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.
    15. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2024. "Autoregressive conditional betas," Journal of Econometrics, Elsevier, vol. 238(2).

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    More about this item

    Keywords

    Cholesky decomposition; Integrated covariance; Non-synchronous trading; Positive semidefinite; Realized covariance;
    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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