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A New Parametrization of Correlation Matrices

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  • Ilya Archakov
  • Peter Reinhard Hansen

Abstract

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in Rn(n−1)/2 is provided, and we derive its numerical complexity.

Suggested Citation

  • Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:4:p:1699-1715
    DOI: 10.3982/ECTA16910
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    10. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org.
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    Cited by:

    1. K. B. Gubbels & J. Y. Ypma & C. W. Oosterlee, 2023. "Principal Component Copulas for Capital Modelling," Papers 2312.13195, arXiv.org.
    2. Ilya Archakov & Peter Reinhard Hansen & Yiyao Luo, 2022. "A New Method for Generating Random Correlation Matrices," Papers 2210.08147, arXiv.org.
    3. Ayed Alwadain & Rao Faizan Ali & Amgad Muneer, 2023. "Estimating Financial Fraud through Transaction-Level Features and Machine Learning," Mathematics, MDPI, vol. 11(5), pages 1-15, February.
    4. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Shin, Minchul, 2023. "Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1054-1086.
    5. 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.
    6. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org.
    7. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    8. Chen Tong & Peter Reinhard Hansen, 2023. "Characterizing Correlation Matrices that Admit a Clustered Factor Representation," Papers 2308.05895, arXiv.org.
    9. Ilya Archakov & Peter Reinhard Hansen, 2020. "A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices," Papers 2012.02698, arXiv.org, revised Nov 2021.
    10. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.

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