Fit (VineCopulaObject)

Estimating objects of the VineCopula class

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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.