The COPULA Procedure (Experimental)

FIT Statement

FIT type <NAME=name><INIT=(parameter-value-options)> /options ;

The FIT statement estimates the parameters for a specified copula type.


specifies the type of the copula to be estimated, which is one of the following:


fits the normal copula


fits the $t$ copula


fits the Clayton copula


fits the Gumbel copula


fits the Frank copula


specifies an identifier for the fit, which is stored as an ID variable in the OUTCOPULA= data set.


provides the initial values for the numerical optimization. For Archimedean copulas, the initial values of the parameter are computed using the calibration method. The initial value for the degrees-of-freedom parameter in the $t$ copula is set to 2.0.

You can specify the following options after a slash (/):


specifies the method used to estimate parameters. MLE represents canonical maximum likelihood estimation (CMLE) or maximum likelihood estimation (MLE). CAL is the calibration method that uses the correlation matrix (only Kendall’s tau is implemented in this procedure). For the $t$ copula, if METHOD=CAL, then the correlation matrix is estimated using the calibration method with Kendall’s tau and the degrees of freedom are estimated by the MLE. For the normal copula, only MLE is supported and METHOD=CAL is ignored. The default for all copula types is METHOD=MLE.


specifies the name of the output data set. Each fitted copula is written to the OUTCOPULA= data set. The data set is not created if this option is not specified.


specifies the output data set for saving the pseudo-samples with uniform marginal distributions. The pseudo-samples are obtained by transforming the individual variables of the original data with the empirical cumulative distribution functions (CDFs). The data set is not created if this option is not specified.


specifies the marginal distribution of the individual variables. If MARGINALS=UNIFORM, then the copula is fitted with the input data without transformation. If MARGINALS=EMPIRICAL, the marginal empirical CDF is used to transform the data and the copula is fitted using the transformed data.

PLOTS<(global-plot-options)> < = specific-plot-options>

controls the plots that are produced by the COPULA procedure. By default, PROC COPULA produces a scatter plot matrix for variables (that is, it displays a symmetric matrix plot with the variables that are specified in the VAR statement).

You can specify the following global-plot-options:


requests scatter plots for pairs of variables. If you specify this option, PROC COPULA displays a scatter plot for each applicable pair of distinct variables that are specified in the VAR statement.


specifies the maximum number of variables specified in the VAR statement to be displayed in the matrix plot. The NVAR=ALL option uses all variables that are specified in the VAR statement. By default, NVAR=5.

You can specify the following specific-plot-options:


requests the data type to be plotted. DATA=ORIGINAL presents the data in its original marginal distribution; DATA=UNIFORM shows the transformed data with uniform marginal distribution; and DATA=BOTH plots both the original and uniform data types. If MARGINALS=UNIFORM, then the transformation is omitted and the DATA= option is ignored.


suppresses all plots.

Printing Options


prints a summary iteration listing.


default option.


suppresses the correlation matrix.


suppresses all output.