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Tyler’s M-Estimator in High-Dimensional Financial-Data Analysis

In: Modern Nonparametric, Robust and Multivariate Methods

Author

Listed:
  • Gabriel Frahm

    (Helmut Schmidt University/University of the Federal Armed Forces Germany, Department of Mathematics/Statistics)

  • Uwe Jaekel

    (University of Applied Sciences Koblenz, Department of Mathematics and Technology)

Abstract

Standard methods of random matrix theory have been often applied to high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory by taking the stylized facts of empirical finance into consideration. In particular, the Marčenko–Pastur law generally fails when analyzing the spectral distribution of the sample covariance matrix if the data are generalized spherically distributed and heavy tailed. We propose Tyler’s M-estimator as an alternative. Substituting the sample covariance matrix by Tyler’s M-estimator resolves the typical difficulties that occur in financial-data analysis. In particular, the Marčenko–Pastur law remains valid. This holds even if the data are not generalized spherically distributed but independent and identically distributed.

Suggested Citation

  • Gabriel Frahm & Uwe Jaekel, 2015. "Tyler’s M-Estimator in High-Dimensional Financial-Data Analysis," Springer Books, in: Klaus Nordhausen & Sara Taskinen (ed.), Modern Nonparametric, Robust and Multivariate Methods, edition 1, chapter 0, pages 289-305, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22404-6_17
    DOI: 10.1007/978-3-319-22404-6_17
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