Matrix moments in a real, doubly correlated algebraic generalization of the Wishart model

@article{Guhr2020MatrixMI,
  title={Matrix moments in a real, doubly correlated algebraic generalization of the Wishart model},
  author={Thomas Guhr and Andreas Schell},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={54}
}
  • T. GuhrA. Schell
  • Published 15 November 2020
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
The Wishart model of random covariance or correlation matrices continues to find ever more applications as the wealth of data on complex systems of all types grows. The heavy tails often encountered prompt generalizations of the Wishart model, involving algebraic distributions instead of a Gaussian. The mathematical properties pose new challenges, particularly for the doubly correlated versions. Here we investigate such a doubly correlated algebraic model for real covariance or correlation… 
View on IOP Publishing
iopscience.iop.org
4 Citations
Background Citations
1
Methods Citations
1

4 Citations

Exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations of covariances or correlations

  • T. GuhrA. Schell
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate.…

Local tail statistics of heavy-tailed random matrix ensembles with unitary invariance

We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating question has been…

A rate of convergence when generating stable invariant Hermitian random matrix ensembles

This work considers a sum of a specific construction of identically and independently distributed random matrices that are based on Haar distributed unitary matrices and a stable random vectors and derives the rate of convergence in the supremums norm and shows that this rate is optimal in the class of all stable invariantrandom matrices for a fixed stability exponent.

Stable distributions and domains of attraction for unitarily invariant Hermitian random matrix ensembles

We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary…

References

SHOWING 1-10 OF 41 REFERENCES

Eigenvalue density of the doubly correlated Wishart model: exact results

Data sets collected at different times and different observing points can possess correlations at different times and at different positions. The doubly correlated Wishart model takes both into…

Spectral moments of correlated Wishart matrices.

The method gives exact analytic relations between the spectral moments and the eigenvalue densities of the covariance matrices and their estimators and can be used in practice to extract the information about genuine correlations from the given experimental realization of random matrices.

Power law deformation of Wishart–Laguerre ensembles of random matrices

We introduce a one-parameter deformation of the Wishart–Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed…

The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy

The exact density of states of empirical correlation matrices that generalizes the Marcenko-Pastur result is established and the Kullback-Leibler entropies of empirical Student matrices are found to be independent of the true correlation matrix, as in the Gaussian case.

Exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations of covariances or correlations

  • T. GuhrA. Schell
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate.…

Eigenvalue density of correlated complex random Wishart matrices.

  • S. SimonA. L. Moustakas
  • Mathematics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M)…

Constructing analytically tractable ensembles of stochastic covariances with an application to financial data

This work presents a method to derive the distribution of the covariances from the Distribution of the amplitudes, and applies this method to financial returns where large amounts of data are available.

Negative moments of characteristic polynomials of random matrices: Ingham–Siegel integral as an alternative to Hubbard–Stratonovich transformation

Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying…

Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of…