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High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market

Author

Listed:
  • Azam Kheyri

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa)

  • Andriette Bekker

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa)

  • Mohammad Arashi

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa
    Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran)

Abstract

This article studies the estimation of the precision matrix of a high-dimensional Gaussian network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize a penalized likelihood function where the elastic net-type penalty is considered as a combination of a norm-one penalty and a targeted Frobenius norm penalty. Numerical illustrations demonstrate that our proposed methodology is a competitive candidate for high-dimensional precision matrix estimation compared to some existing alternatives. We demonstrate the relevance and efficiency of GSOS using a foreign exchange markets dataset and estimate dependency networks for 32 different currencies from 2018 to 2021.

Suggested Citation

  • Azam Kheyri & Andriette Bekker & Mohammad Arashi, 2022. "High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4232-:d:970978
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    References listed on IDEAS

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    1. van Wieringen, Wessel N. & Peeters, Carel F.W., 2016. "Ridge estimation of inverse covariance matrices from high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 284-303.
    2. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
    3. Daniel J. Fenn & Mason A. Porter & Peter J. Mucha & Mark McDonald & Stacy Williams & Neil F. Johnson & Nick S. Jones, 2012. "Dynamical clustering of exchange rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1493-1520, October.
    4. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    5. Basnarkov, Lasko & Stojkoski, Viktor & Utkovski, Zoran & Kocarev, Ljupco, 2019. "Correlation patterns in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1026-1037.
    6. Warton, David I., 2008. "Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 340-349, March.
    7. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    8. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    9. Lingzhou Xue & Shiqian Ma & Hui Zou, 2012. "Positive-Definite ℓ 1 -Penalized Estimation of Large Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1480-1491, December.
    10. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    11. Shan, Liang & Kim, Inyoung, 2018. "Joint estimation of multiple Gaussian graphical models across unbalanced classes," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 89-103.
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