I am quite new to copula models. The main idea of the copula is based on the Sklar's theorem. In copula models, we first need to transform the data to copula data (standard uniform [0,1]). Then, we can apply our model to estimates the model parameters. After that, we need to back to the original data using inverse cumulative distribution function. My question is, why do we need the last step while we already have our original data?
For example,
Also, Sklar's theorem stated that.
$C(u_1, u_2) = F(F_1^{(-1)} (u_1), F_2^{(-1)} (u_2))$