estimate_skew_t {highOrderPortfolios}

Estimate the parameters of skew-t distribution from multivariate observations

Description

Using the package fitHeavyTail to estimate the parameters of ghMST distribution from multivariate observations, namely, location vector (mu), skewness vector (gamma), scatter matrix (scatter), degree of freedom (nu), parameters a, and the Cholesky decomposition of the scatter matrix (chol_Sigma).

Usage

estimate_skew_t(
  X,
  initial = NULL,
  nu_lb = 9,
  max_iter = 100,
  ptol = 0.001,
  ftol = Inf,
  PXEM = TRUE,
  return_iterates = FALSE,
  verbose = FALSE
)

Arguments

X

Data matrix containing the multivariate time series (each column is one time series).

initial

List of initial values of the parameters for the iterative estimation method. Possible elements include:

• nu: default is 4,

• mu: default is the data sample mean,

• gamma: default is the sample skewness vector,

• scatter: default follows from the scaled sample covariance matrix,

nu_lb

Minimum value for the degree of freedom to maintain the existence of high-order moments (default is 9).

max_iter

Integer indicating the maximum number of iterations for the iterative estimation method (default is 100).

ptol

Positive number indicating the relative tolerance for the change of the variables to determine convergence of the iterative method (default is 1e-3).

ftol

Positive number indicating the relative tolerance for the change of the log-likelihood value to determine convergence of the iterative method (default is Inf, so it is not active). Note that using this argument might have a computational cost as a convergence criterion due to the computation of the log-likelihood (especially when X is high-dimensional).

PXEM

Logical value indicating whether to use the parameter expansion (PX) EM method to accelerating the convergence.

return_iterates

Logical value indicating whether to record the values of the parameters (and possibly the log-likelihood if ftol < Inf) at each iteration (default is FALSE).

verbose

Logical value indicating whether to allow the function to print messages (default is FALSE).

Value

A list containing the following elements:

mu

Location vector estimate (not the mean).

gamma

Skewness vector estimate.

scatter

Scatter matrix estimate.

nu

Degrees of freedom estimate.

chol_Sigma

Choleski decomposition of the Scatter matrix estimate.

a

A list of coefficients useful for later computation

Author(s)

Xiwen Wang, Rui Zhou, and Daniel P. Palomar

References

Aas, Kjersti and Ingrid Hobæk Haff. "The generalized hyperbolic skew student’st-distribution," Journal of financial econometrics, pp. 275-309, 2006.

Examples

library(highOrderPortfolios)
data("X50")
X_skew_t_params <- estimate_skew_t(X50)