Estimating objects of the VineCopula class
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.
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)
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.
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.