Let , and let be a univariate t distribution with degrees of freedom.
The Student’s t copula can be written as
where is the multivariate Student’s t distribution that has a correlation matrix with degrees of freedom.
The input parameters for the simulation are . The t copula can be simulated by the following steps:
Generate a multivariate vector that follows the centered t distribution with degrees of freedom and correlation matrix .
Transform the vector into , where is the distribution function of univariate t distribution with degrees of freedom.
To simulate centered multivariate t random variables, you can use the property that if , where and the univariate random variable .