Copula-Based Multivariate Input Models for Stochastic Simulation

Abstract

As large-scale discrete-event stochastic simulation becomes a tool that is used routinely for the design and analysis of stochastic systems, the need for input-modeling support with the ability to represent complex interactions and interdependencies among the components of multivariate time-series input processes is more critical than ever. Motivated by the failure of independent and identically distributed random variables to represent such input processes, a comprehensive framework called Vector-Autoregressive-To-Anything (VARTA) has been introduced for multivariate time-series input modeling. Despite its flexibility in capturing a wide variety of distributional shapes, we show that VARTA falls short in representing dependence structures that arise in situations where extreme component realizations occur together. We demonstrate that it is possible to extend VARTA to work for such dependence structures via the use of the copula theory, which has been used primarily for random vectors in the simulation input-modeling literature, for multivariate time-series input modeling. We show that our copula-based multivariate time-series input model, which includes VARTA as a special case, allows the development of statistically valid fitting and fast sampling algorithms well suited for driving large-scale stochastic simulations.