Explanation

Let's analyze each statement:

Statement I: Correct

• Copula functions allow us to model the dependence structure separately from the marginal distributions. This is a key advantage of copulas - they decouple the dependence structure from the marginal distributions.

Statement II: Incorrect

• Transformation of variables can change their correlation structure. For example, nonlinear transformations can alter the correlation between variables.

Statement III: Incorrect

• Correlation requires that the variables have finite variances. If a distribution doesn't have a defined variance (like some heavy-tailed distributions), correlation is not well-defined and cannot be a useful measure.

Statement IV: Correct

• Correlation is indeed a good measure of dependence for multivariate elliptical distributions (such as the multivariate normal distribution), where it captures the complete dependence structure.

Therefore, only statements I and IV are correct, making option A the correct answer.