The COPULA Procedure

specifies the data set that contains the correlation matrix to use for elliptical copulas. If the correlation matrix is valid but its elements are not submitted in order, then you must provide the variable names in the first column of the matrix, and these names must match the variable names in the VAR statement. For an example of a correlation matrix input in this form, see Output 11.2.1. If the correlation matrix elements are submitted in order, the first column of variable names is not required. You can use this option for normal and t copulas.

specifies the degrees of freedom. You can use this option for t copulas.

specifies the hierarchy for hierarchical Archimedean copulas. The argument usually consists of multiple specification lines, where each line specifies one copula in the hierarchy. The name can be user-defined symbols, with the exception of the copula at the top of the hierarchy, which must be named ROOT. The HAC-specification is a list of symbols that can be either defined copula names or variable names from the VAR statement, depending on whether the element of the copula is a variable or an inner copula in the hierarchy. For example, you can use the following code to define a hierarchical Archimedean copula, with the hierarchy shown in Figure 5:

var u1-u4;
define cop hacclayton hierarchy=(
root = (c1 c2)(theta=1)
c1 = (u1 u2)(theta=3)
c2 = (u3 u4)(theta=5));

Note that as long as the specification is valid, the order of the specification lines does not matter. In the previous example, you could first list and , and then define .

specifies the data set that contains the correlation matrix defined in Kendall’s tau. If the correlation matrix is valid but its elements are not submitted in order, then you must provide the variable names in the first column of the matrix, and these names must match the variable names in the VAR statement. If the correlation matrix elements are submitted in order, the first column of variable names is not required. You can use this option for normal and t copulas.

specifies the data set that contains the correlation matrix defined in Spearman’s rho. If the correlation matrix is valid but its elements are not submitted in order, then you must provide the variable names in the first column of the matrix, and these names must match the variable names in the VAR statement. If the correlation matrix elements are submitted in order, the first column of variable names is not required. You can use this option for normal copulas.

specifies the parameter value for Archimedean copulas.