# Fit (VineCopulaObject)

Estimating objects of the VineCopula class

## Purpose

The function computes ML-estimates for the parameters of a simplified vine copula. Therefore, first starting values for the joint estimation are obtained by iteratively estimating the pair-copulas in the first trees and using those estimates to obtain the arguments for the copulas in the second tree. Then the pair-copulas in the second tree are estimated and so on. These estimated parameters from the sequential procedure are then used to obtained the ML-estimates, by minimizing the overall negative log-likelihood of the whole vine copula numerically.

## Usage

```
Estimating a simplified vine copula (joint estimation;
the default method)
VineCopulaHat = Fit(VineCopulaObject,u)
VineCopulaHat = Fit(VineCopulaObject,u,'joint')
Estimating a simplified vine copula (sequential
estimation)
VineCopulaHat = Fit(VineCopulaObject,u,'sequential')
Estimating a simplified vine copula (with a cut off
tree / truncation level)
VineCopulaHat = Fit(VineCopulaObject,u,EstMethod,CutOffTree)
```

## Inputs

```
VineCopulaObject= An object from the class VineCopula.
u = A (n x d) dimensional vector of
values lying in [0,1] (the
observations).
EstMethod = The estimation method must be either
'joint' or 'sequential'. If it is
not explicitly given, a joint
estimation is performed (default).
CutOffTree = The CutOffTree (or also called
truncation level) can be used to set
all pair-copulas from the (CutOffTree
+ 1)-th tree on to independence
copulas (i.e., ignore them in the
joint estimation). The CutOffTree
does only influence the joint
estimation.
```

## Outputs

```
VineCopulaHat = An object from the class VineCopula.
The sequential estimates are stored
in VineCopulaHat.SeqEstParameters,
the estimated parameters from the
joint estimation are stored in
VineCopulaHat.parameters and the two
maximized values of the vine copula
log-likelihood are stored in
VineCopulaHat.MaxLLs.
```