The COPULA Procedure (Experimental)
- Overview
- Getting Started
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Syntax
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Details
Sklar’s Theorem Dependence Measures Normal Copula Student’s t copula Archimedean Copulas Canonical Maximum Likelihood Estimation (CMLE) Exact Maximum Likelihood Estimation (MLE) Calibration Estimation Nonlinear Optimization Options Displayed Output OUTCOPULA= Data Set OUTPSEUDO=, OUT=, and OUTUNIFORM= Data Sets ODS Table Names ODS Graph Names
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Examples
- References
| FIT Statement |
- FIT type <NAME=name><INIT=(parameter-value-options)> /options ;
The FIT statement estimates the parameters for a specified copula type.
- type
-
specifies the type of the copula to be estimated, which is one of the following:
- NORMAL
fits the normal copula
- T
fits the
copula - CLAYTON
fits the Clayton copula
- GUMBEL
fits the Gumbel copula
- FRANK
fits the Frank copula
- NAME=name
specifies an identifier for the fit, which is stored as an ID variable in the OUTCOPULA= data set.
- INIT=(parameter-value-options)
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
copula is set to 2.0.
- METHOD=MLE | CAL
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
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. - OUTCOPULA=SAS-data-set
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.
- 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 with the empirical cumulative distribution functions (CDFs). The data set is not created if this option is not specified.
- MARGINALS=UNIFORM | EMPIRICAL
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<=plot-request>
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controls the plots that are produced by the COPULA procedure. You can specify any of the following plot-requests:
- DATA=ORIGINAL | UNIFORM | BOTH
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.
- MATRIX <( matrix-options )>
requests a scatter plot matrix for variables. That is, the procedure displays a symmetric matrix plot with the variables that are specified in the VAR statement.
- SCATTER <(scatter-options)>
requests scatter plots for pairs of variables. That is, the procedure displays a scatter plot for each applicable pair of distinct variables that are specified in the VAR statement.
By default, PLOTS=MATRIX: a scatter plot matrix for all variables is displayed.
The available matrix-options and scatter-options are as follows:- NVAR=ALL | n
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.