# PairCopulaAIC

Computing the AIC of a pair-copula

## Purpose

The function computes the value of the AIC for a copula for a given matrix of observations u, which have to lie in the 2-dimensional unit cube, evaluated at the ML estimates. Possible pair-copula families:

``````       0   Indep
1   AMH
2   AsymFGM
3   BB1
4   BB6
5   BB7
6   BB8
7   Clayton
8   FGM
9   Frank
10  Gaussian
11  Gumbel
12  IteratedFGM
13  Joe
14  PartialFrank
15  Plackett
16  Tawn1
17  Tawn2
18  Tawn
19  t
``````

## Usage

``````    [AIC,ParamHat] = PairCopulaAIC(family,u1,u2)
Rotated pair-copulas
[AIC,ParamHat] = PairCopulaAIC(family,u1,u2,roatation)
``````

## Inputs

``````   family          = The copula family.
u1              = A (n x 1) dimensional vector of values lying in [0,1].
u2              = A (n x 1) dimensional vector of values lying in [0,1].
rotation        = The degree of rotation, i.e., either 90, 180 or
270. No rotation is achieved by letting the
rotation argument empty or by choosing 0
rotation.
``````

## Outputs

``````  AIC              = The value of the AIC evaluated at the ML-estimator.
ParamHat         = The ML-estimate for the parameter vector.
``````