The COPULA Procedure
- Overview
- Getting Started
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Syntax
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DetailsSklar’s TheoremDependence MeasuresNormal CopulaStudent’s t copulaArchimedean CopulasCanonical Maximum Likelihood Estimation (CMLE)Exact Maximum Likelihood Estimation (MLE)Calibration EstimationNonlinear Optimization OptionsDisplayed OutputOUTCOPULA= Data SetOUTPSEUDO=, OUT=, and OUTUNIFORM= Data SetsODS Table NamesODS Graph Names
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Examples
- References
DEFINE name copula-type < ( parameter-value-options ... ) > ;
The DEFINE statement specifies the relevant information of the copula used for the simulation.
- name
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specifies the name of the copula definition, which can be used later in the SIMULATE statement.
- copula-type
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specifies one of the following types of the copula:
- NORMAL
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specifies the normal copula.
- T
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specifies the
copula.
- CLAYTON
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specifies the Clayton copula.
- GUMBEL
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specifies the Gumbel copula.
- FRANK
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specifies the Frank copula.
These copula models are also described in the section Details: COPULA Procedure.
- parameter-value-options
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specify the input parameters used to simulate the specified copula. These options must be appropriate for the type of copula specified. The following options are valid:
- CORR=SAS-data-set
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specifies the data set that contains the correlation matrix to use for elliptical copulas. If the correlation matrix is valid but 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. See Output 10.2.1 for an example of a correlation matrix input in this form. If the correlation matrix is submitted in order, the first column of variable names is not required. This option can be used for the normal and
copulas.
- KENDALL=SAS-data-set
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specifies the data set that contains the correlation matrix defined in Kendall’s tau. If the correlation matrix is valid but 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 is submitted in order, the first column of variable names is not required. This option can be used for the normal and
copulas.
- SPEARMAN=SAS-data-set
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specifies the data set that contains the correlation matrix defined in Spearman’s rho. If the correlation matrix is valid but 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 is submitted in order, the first column of variable names is not required. This option can be used for the normal copula.
- DF=value
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specifies the degrees of freedom. This option can be used for the
copula.
- THETA=value
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specifies the parameter value for the Archimedean copulas.
The DEFINE statement is used with the SIMULATE statement.The FIT statement can also be used with the SIMULATE statement. The results of the FIT statement can be the input of the SIMULATE statement. Therefore, the SIMULATE statement can follow the FIT statement.If there is no FIT statement, then the DEFINE statement must precede SIMULATE statement. However, the FIT and DEFINE statements cannot both be used in the same procedure.