Copulas 3.3 - fitting copulas using maximum likelihood estimation

[@Tyokok]

Great Thanks to you!

[@sumandhamala4807]

Thankyou so much.

[@Daniel88santos]

Hello I have a doubt that maybe you can answer me: I want to make Monte Carlo simulations with two dependent variables. The two variables don't follow a normal distribution and both have fat tails. I've seen that Cholesky decomposition is a way to do it, but one constrain is that it needs the a covariance matrix which uses the Pearson's Rho correlation value, and this correlation method is not robust against fat tailed data. So the questions are: 1) Do you know if I can use for the covariance matrix the kendall's tau value and then apply Cholesky Decomposition? 2) If 1) isn't valid, because the maths doesn't hold, do you know if Copulas are the solution? I'm not understand after I reach the copula how then I can apply it, for example in a Monte Carlo simulation. Can you show in one of your future videos a full process, from the moment that we pick our two datasets, and obtain the dependence between them (having in consideration they are fat tailed) and finally how to pick the copula obtained and apply it to a Monte Carlo simulation to create the two depend paths? Best regards, Daniel.

[@PaulSweeting]

Hi, thanks for your question. I talk about the correlation issue in "Copulas 3.2". In a nutshell, you could re-scale the marginals so they're normal and calculate Pearson's rho. This would give a positive semi-definite matrix, but no information on the distribution of the correlations. This is ok for a Gaussian copula, in my view. Forna t-copula, it's the same process, but stretching the marginals to the appropriate t distribution before the correlation calculation. Or you can use the Kendall's tau to Spearman's rho approach. You could even find the correlations by MLE! In any case, you could plug the results into various log likelihood functions to see what gives the best fit using (e.g.) LR test or BIC (if between Gaussian and t) or AIC (between different t). But a key question is: how sensitive are your conclusions to getting the correlations exactly right? Would the choice of approach change the matrix by more than (e.g.) adding an extra month of data? Hope this helps!

[@PaulSweeting]

(Also, working on the simulation talk - will record it shortly...)