Parameterization of Copulas and Covariance Decay of Stochastic Processes

TL;DR

This paper develops a method to construct stochastic processes with specific covariance decay properties by parameterizing marginals and copulas, providing a flexible framework applicable to various models including Gaussian and Euclidean copulas.

Contribution

It introduces a compatibility-free methodology for constructing processes with desired covariance decay using copula parameterization, expanding modeling options in stochastic process theory.

Findings

Methodology is compatibility-free.

Includes examples with Gaussian and Euclidean copulas.

Links theory to applied time series models.

Abstract

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.