Parameterization of Copulas and Covariance Decay of Stochastic Processes

In this work we study the problem of constructing stochastic processes with a predetermined covariance decay by parameterizing its marginals and a given family of copulas. We show that the proposed methodology is compatibility-free and present several examples to illustrate the theory, including the important Gaussian and Euclidean families of copulas. We associate the theory to common applied time series models.