Simulation of Univariate Time Series Using Copulas

In this work we review and study some problems related to simulation of univariate time series based on some prescribed copula. We give some examples in the context of copula-based semiparametric models as in Chen and Fan (2006). We adapt some results to cover the case of the Brownian motion. Our approach allows one to simulate processes which behaves like a Brownian motion but have arbitrary marginals.