sample_dvine {Surrogate}

Sample copula data from a given four-dimensional D-vine copula

Description

sample_dvine() is a helper function that samples copula data from a given D-vine copula. See details for more information on the parameterization of the D-vine copula.

Usage

sample_dvine(
  copula_par,
  rotation_par,
  copula_family1,
  copula_family2 = copula_family1,
  n
)

Arguments

copula_par

Parameter vector for the sequence of bivariate copulas that define the D-vine copula. The elements of copula_par correspond to (c_{12}, c_{23}, c_{34}, c_{13;2}, c_{24;3}, c_{14;23}).

rotation_par

Vector of rotation parameters for the sequence of bivariate copulas that define the D-vine copula. The elements of rotation_par correspond to (c_{12}, c_{23}, c_{34}, c_{13;2}, c_{24;3}, c_{14;23}).

copula_family1

Copula family of c_{12} and c_{34}. For the possible options, see loglik_copula_scale(). The elements of copula_family correspond to (c_{12}, c_{34}).

copula_family2

Copula family of the other bivariate copulas. For the possible options, see loglik_copula_scale(). The elements of copula_family2 correspond to (c_{23}, c_{13;2}, c_{24;3}, c_{14;23}).

n

Number of samples to be taken from the D-vine copula.

Value

A n \times 4 matrix where each row corresponds to one sampled vector and the columns correspond to U_1, U_2, U_3, and U_4.

D-vine Copula

Let \boldsymbol{U} = (U_1, U_2, U_3, U_4)' be a random vector with uniform margins. The corresponding distribution function is then a 4-dimensional copula. A D-vine copula as a family of k-dimensional copulas. Indeed, a D-vine copula is a k-dimensional copula that is constructed from a particular product of bivariate copula densities. In this function, only 4-dimensional copula densities are considered. Under the simplifying assumption, the 4-dimensional D-vine copula density is the product of the following bivariate copula densities:

• c_{12}, c_{23}, and c_{34}

• c_{13;2} and c_{24;3}

• c_{14;23}