Regular Vine Copula Construction

In 3 variables regular vine construction, we have $$f(x_1,x_2,x_3) = \text{marginal}\times\text{unconditional pairs}\times\text{conditional pairs}=f_3(x_3)f_2(x_2)f_1(x_1)\times c_{12}(F_1(x_1),F_2(x_2))c_{23}(F_2(x_2),F_3(x_3))\times c_{13\vert2}(F_{1\vert2}(x_1\vert x_2),F_{3\vert2}(x_3\vert x_2))$$ Using RVineMLE in R VineCopula package, only the marginal (uniform) and unconditional pairs are required for input. How does it determine what $$c_{13\vert2}$$ to be used for MLE construction ?

It does not seems clear to me how the conditional pair copula functions are constructed even after reading Parameter estimation for pair-copula constructions (Ingrid, 2013).

In RVineMLE you need to specify all copula families for each pair of variables. VineCopula package is free from estimating the margins. So, what you need to do is:

1- If you are working on real data, then you need to make sure it is transformed to copula data.

2- Then you need to specify the matrix for each of (1) copula family and (2) their corresponding parameters (if you only use one-parametric copula).

3- Then you need to fit the model to your data.

RVineMLE estimate the parameters jointly.

Hope this help.

• Thanks. But up to step 2 you are still fitting the unconditional copula pair, the conditional ones are unspecified. Looking at the code of rvinemle it looks like they use the function Bicopest to do that. Hope someone can verify this the case. Commented Mar 14, 2019 at 10:01
• @kchpchan, I think you misunderstood me. For RvineMLE you need to specify all the involved copulas prior to start the model. For this case, you can use RvineSeqEs to specify the pair-copulas for your data and then use RvineMLE method. Bicopest estimates the parameters. there is another function to select the copulas. Commented Mar 18, 2019 at 4:00
• RvineSeqEst specifies the pair-copulas tree-by-tree. Similar to RVineMLE you need to specify all the involved pair-copulas. RVineStructureSelect can do all the job for you tree-by-tree. Commented Mar 18, 2019 at 4:02