estimate_sample_moments {highOrderPortfolios}

Estimate first four moment parameters of multivariate observations

Description

Estimate first four moments of multivariate observations, namely, mean vector, covariance matrix, coskewness matrix, and cokurtosis matrix.

Usage

estimate_sample_moments(X, adjust_magnitude = FALSE)

Arguments

X

Data matrix.

adjust_magnitude

Boolean indicating whether to adjust the order of magnitude of parameters. Note: this is specially designed for the function design_MVSKtilting_portfolio_via_sample_moments().

Value

A list containing the following elements:

mu

Mean vector.

Sgm

Covariance matrix.

Phi_mat

Co-skewness matrix.

Psi_mat

Co-kurtosis matrix.

Phi

Co-skewness matrix in vector form (collecting only the unique elements).

Psi

Co-kurtosis matrix in vector form (collecting only the unique elements).

Phi_shred

Partition on Phi (see reference).

Psi_shred

Partition on Psi (see reference).

Author(s)

Rui Zhou and Daniel P. Palomar

References

R. Zhou and D. P. Palomar, "Solving High-Order Portfolios via Successive Convex Approximation Algorithms," in IEEE Transactions on Signal Processing, vol. 69, pp. 892-904, 2021. <doi:10.1109/TSP.2021.3051369>.

Examples

library(highOrderPortfolios)
data(X50)

X_moments <- estimate_sample_moments(X50[, 1:10])