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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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