makePsd: Returns the positive semidefinite projection of a symmetric...

In jonathancornelissen/highfrequency: Tools for Highfrequency Data Analysis

Returns the positive semidefinite projection of a symmetric matrix using the eigenvalue method

Description

Function returns the positive semidefinite projection of a symmetric matrix using the eigenvalue method.

Usage

makePsd(S, method = "covariance")

Arguments

S	a non-PSD matrix.
method	character, indicating whether the negative eigenvalues of the correlation or covariance should be replaced by zero. Possible values are "covariance" and "correlation".

Details

We use the eigenvalue method to transform S into a positive semidefinite covariance matrix (see, e.g., Barndorff-Nielsen and Shephard, 2004, and Rousseeuw and Molenberghs, 1993). Let Γ be the orthogonal matrix consisting of the p eigenvectors of S. Denote λ_1^+,…,λ_p^+ its p eigenvalues, whereby the negative eigenvalues have been replaced by zeroes. Under this approach, the positive semi-definite projection of S is S^+ = Γ' \mbox{diag}(λ_1^+,…,λ_p^+) Γ.

If method = "correlation", the eigenvalues of the correlation matrix corresponding to the matrix S are transformed, see Fan et al. (2010).

Value

A matrix containing the positive semi definite matrix.

Author(s)

Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

References

Barndorff-Nielsen, O. E. and Shephard, N. (2004). Measuring the impact of jumps in multivariate price processes using bipower covariation. Discussion paper, Nuffield College, Oxford University.

Fan, J., Li, Y., and Yu, K. (2012). Vast volatility matrix estimation using high frequency data for portfolio selection. Journal of the American Statistical Association, 107, 412-428

Rousseeuw, P. and Molenberghs, G. (1993). Transformation of non positive semidefinite correlation matrices. Communications in Statistics - Theory and Methods, 22, 965-984.

jonathancornelissen/highfrequency documentation built on Jan. 10, 2023, 7:29 p.m.