Generating Copula‐Correlated Random Variables: A Sequential Acceptance‐Rejection Method

ABSTRACT In this paper, we consider the problem of generating a random vector whose joint distribution is characterized by a copula function and their marginal distribution functions. We propose a sequential acceptance‐rejection method, which avoids the inversion of both marginal distributions and conditional distributions of the copula function which are needed in traditional generation methods. In our method, we first generate samples based on the marginal distributions and then use an acceptance‐rejection procedure to construct samples with the desired dependence structure. The method is also applicable in generating time series random variables. We prove that the computational cost of our method only grows linearly to their dimensionality for several types of copulas. Finally, we provide extensive numerical experiments which show our method is quite efficient in comparison with traditional methods.