Tools for dependent simulation input with Copulas

Abstract

Copulas encompass the entire dependence structure of multivariate distributions, and not only the correlations. Together with the marginal distributions of the vector elements, they define a multivariate distribution which can be used to generate random vectors with this distribution. A toolbox is presented which implements input models with this method, for random vectors and time series. Time series are modeled with some general autoregressive processes. The copulas are estimated from observed samples of random vectors. The MATLAB tool calculates the copula, generates random vectors and time series, and provides statistics and diagrams which indicate validity and accuracy of the input model. It is fast and allows for random vectors with high dimensions, for example 100. For this efficiency an intricate data structure is essential. The generation algorithm is also implemented with Java methods.