The CCOPULA Procedure
FIT Statement
FIT type <NAME=name><INIT=(parameter-value-options>) / options;
The FIT statement estimates the parameters for a specified copula type.
You must specify a type:
- type
specifies the type of the copula to be estimated, which is one of the following:
- CLAYTON
fits the Clayton copula.
- FRANK
fits the Frank copula.
- GUMBEL
fits the Gumbel copula.
- NORMAL
fits the normal copula.
- T
fits the t copula.
You can also specify the following options:
- INIT=(parameter-value-options)
provides the initial values for the numerical optimization.
[parameter-value-options] specify the input parameters that are used to initialize the specified copula. These options must be appropriate for the type of copula that you specify. You can specify the following options:
- CORR=SAS-data-set
specifies the data set that contains the correlations matrix to use for elliptical copulas. All columns of the matrix must be numeric. The order of the column names in the matrix must match their order in the VAR statement. The order of the rows must be such that row n contains the correlations between the nth variable in the VAR statement and the other variables. You can use this option for t copulas.
- DF=value
specifies the degrees of freedom. You can use this option for t copulas.
- KENDALL=SAS-data-set
specifies the data set that contains the correlations matrix defined in Kendall’s tau. All columns of the matrix must be numeric. The order of the column names in the matrix must match their order in the VAR statement. The order of the rows must be such that row n contains the correlations between the nth variable in the VAR statement and the other variables. You can use this option for t copulas.
- SPEARMAN=SAS-data-set
specifies the data set that contains the correlations matrix defined in Spearman’s rho. All columns of the matrix must be numeric. The order of the column names in the matrix must match their order in the VAR statement. The order of the rows must be such that row n contains the correlations between the nth variable in the VAR statement and the other variables. You can use this option for t copulas.
- THETA=value
specifies the parameter value for Archimedean copulas.
For Archimedean copulas, the default initial values of the parameter are computed using the calibration method. The default initial value of the degrees-of-freedom parameter in the t copula is set to 2.0. The following statement shows an initialization for Student’s t copula, where the Kendall’s tau correlations matrix is stored in the
mycas.corrmatdata set and the is set to 2.5:fit t init=(df=2.5 kendall=mycas.corrmat);
- NAME=name
specifies an identifier for the fit.
You can specify the following options after a slash (/):
- MARGINALS=UNIFORM | EMPIRICAL
specifies the marginal distribution of the individual variables. You can specify the following values:
- EMPIRICAL
uses the marginal empirical CDF to transform the data and uses the transformed data to fit the copula.
- UNIFORM
uses the input data without transformation to fit the copula.
- METHOD=MLE | CAL
specifies the method to use to estimate parameters. You can specify the following values:
- CAL
specifies the calibration method that uses the correlations matrix (only Kendall’s tau is implemented in this procedure).
- MLE
specifies canonical maximum likelihood estimation (CMLE) or maximum likelihood estimation (MLE).
For the t copula, if METHOD=CAL, then the correlations 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 METHOD=MLE is supported and METHOD=CAL is ignored. By default for all copula types, METHOD=MLE.
- OUTPSEUDO=SAS-data-set
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 by using the empirical cumulative distribution functions (CDFs). The data set is not created if you omit this option.
- STORE=SAS-item-store
specifies the item store that preserves the properties of the model and the fit results.
Printing Options