If we look at the AIC formula:
AIC = -2*log(ML) + 2k
where k is the number of parameters in the model and is considered as the 'penalizing term' for complexity or over-fitting. Does this assumption of complexity/over-fitting actually apply to copulas? In terms of other models, like a simple linear regression model, I understand that adding more parameters always increases your model's performance so it makes sense to penalize it. But if I fit two copula models to my data, one that has a single parameter (like Clayton copula) and another that has two parameters (like BB1 copula), does that mean the BB1 model should be penalized? What is the intuition behind it specifically in copula models?