From the abstract:

*In this paper, we present copula regression as an alternative to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. In this paper, we will present the formulas and algorithms necessary for conducting a copula regression analysis using the normal copula. However, the ideas presented here can be used with any copula function that can incorporate multiple variables with varying degrees of association.*

In the paper they outline a 3 step process for accomplishing this:

*1) Assume a model for the joint distribution of all the variables (response and covariates)*

*2) Estimate the parameters of the model (the parameters for the selected marginal distributions and the parameters of the copula)*

*3) Compute the predicted values of Y given a set of covariates by using the conditional mean of Y given the covariates.*

I'd also like to point out this interesting virtual course on copula regression from Dr. Edward Frees at the University of Wisconsin: https://sites.google.com/a/wisc.edu/jed-frees/multivariate-regression-using-copulas

I have not had a chance to view these materials in detail, but absolutely think it could be valuable to anyone wanting to learn more about these methods.

**Additional Reading:**

Modeling Dependence with Copulas and R

Copula Based Agricultural Risk Models

Intro to Copulas using SAS

Copulas, R, and the Financial Crisis

**References:**

Parsa, Rahul A, and Stuart A. Klugman, "Copula Regression,"

*Variance*5:1, 2011, pp. 45-54.

Link: http://www.variancejournal.org/issues/?fa=article&abstrID=6831

Link: http://www.variancejournal.org/issues/05-01/45.pdf

Presentation: http://www.casact.org/research/dare/documents/P1-Parsa_1.pdf