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vinepdf.m
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vinepdf.m
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function value = vinepdf(u,A,family,theta)
% Computes the pdf of a simplified vine copula.
%
% call: value = vinepdf(u,A,family,theta)
%
% input x - nxd data matrix of pseudo-observations
% A - a vine array; note that a feasible structure
% has to be used, since the function will not
% check this
% family - a (d-1)x(d-1) cell variable determining the
% copula families used in the calculation;
% possible families: 'gumbel', 'clayton',
% 'frank', 't', 'gauss', 'ind', 'amhaq',
% 'tawn', 'fgm', 'plackett', 'joe',
% 'surclayton', 'surgumbel', 'surjoe'
% theta - a (d-1)x(d-1) cell variable of copula
% parameters; for t-copula insert [rho nu] in
% cell element
%
% output value - nx1 vector of pdf values for each point in u
%
%
% How does it work?
% This function computes the pdf values of points from a given simplified
% vine copula.
%
% Note that for the function to work, the vine array provided by the user
% has to be a feasible vine array in the first place. The function will
% not check feasibilty on its own! For c- and d-vines the function
% cdvinearray can be used to generate a feasible vine array.
%
% Structure of the input is demonstrated for a 5-dimensional r-vine copula:
%
% Let the sample r-vine structure be
%
% 4
% /
% 1 - 2 - 3
% \
% 5
%
% 12 - 23 - 34 - 35
% .
% .
% .
%
% , where the numbers correspond to the columns of the output. In this case
%
% 1 1 2 3 3
% 2 1 2 4
% A = 3 1 2
% 4 1
% 5
%
% is the corresponding vine array.
%
% In order for the function to work, the user has to input information on
% the following bivariate copulas: 12, 23, 34, 35, 13|2, 24|3, 45|3, 14|23,
% 25|34, 15|234, where '|' represents conditioning. Note that this system
% corresponds to the appearance of the copula in the vine array from left
% to right. Input family cell variable for the copulas like this:
%
% family12 family23 family34 family35
% family = family13|2 family24|3 family45|3 0
% family14|23 family25|34 0 0
% family15|234 0 0 0
%
% Matlab syntax:
% family = {'family12','family23','family34','family35'; 'family13|2','family24|3','family45|3',0; 'family14|23','family25|34',0,0;'familiy15|234',0,0,0}
%
%
% Copyright 2020, Maximilian Coblenz
% This code is released under the 3-clause BSD license.
%
% some parsing
p = inputParser;
p.addRequired('u',@ismatrix);
p.addRequired('A',@ismatrix);
p.addRequired('family',@iscell);
p.addRequired('theta',@iscell);
p.parse(u,A,family,theta);
% sanity checks
for ii = 1:1:size(family,1)
for jj = 1:1:size(family,2)-ii+1
if ~cpcheck(family{ii,jj},theta{ii,jj})
error(['invalid parameter for ',family{ii,jj},' copula at (',num2str(ii),',',num2str(jj),')']);
end
end % jj
end % ii
% some sanity checks for vine array A
if (size(A,1) ~= size(A,2))
error('vine array A has to be a quadratic matrix');
end
for jj = 1:1:size(A,1)
if (length(unique(A(1:jj,jj))) ~= jj)
error('input A is not a vine array');
end
end % jj
% Initialize variables
n = size(u,1);
d = size(u,2);
value = ones(n,1);
% start calculation
% permute A, such that a_jj = jj
[A,perm,~] = transforma(A);
u = u(:,perm(:,1));
M = zeros(d);
% compute matrix M
for jj = 2:1:d
for kk = 1:1:jj-1
M(kk,jj) = max(A(1:kk,jj));
end % kk
end % jj
v = cell(d,d);
v_prime = cell(d,d);
for jj = 1:1:d
v{1,jj} = u(:,jj);
v_prime{1,jj} = u(:,jj);
end % jj
% levels 1 to d
for kk = 2:1:d
for ii = 1:1:kk-1
% select correct variables
z1 = v{ii,kk};
if M(ii,kk) == A(ii,kk)
z2 = v{ii,M(ii,kk)};
else
z2 = v_prime{ii,M(ii,kk)};
end
% caluclate pdf
value = value.*copulapdfadv(family{ii,kk-ii},[z2 z1],theta{ii,kk-ii});
% compute pseudo-observations
v{ii+1,kk} = hfunc(z1,z2,family{ii,kk-ii},theta{ii,kk-ii});
v_prime{ii+1,kk} = hfunc(z2,z1,family{ii,kk-ii},theta{ii,kk-ii});
end % ii
end % kk
end