BEKK-GARCH模型之Matlab编程
function [parameters, loglikelihood, Ht, likelihoods, stdresid, stderrors, A, B, scores] = full_bekk_mvgarch(data,p,q, BEKKoptions)
% PURPOSE:
% To Estimate a full BEKK multivariate GARCH model. ****SEE WARNING AT END OF HELP FILE****
%
%
% USAGE:
% [parameters, loglikelihood, Ht, likelihoods, stdresid, stderrors, A, B, scores] = full_bekk_mvgarch(data,p,q,options);
%
%
% INPUTS:
% data - A t by k matrix of zero mean residuals
% p - The lag length of the innovation process
% q - The lag length of the AR process
% options - (optional) Options for the optimization(fminunc)
%
% OUTPUTS:
% parameters - A (k*(k+1))/2+p*k^2+q*k^2 vector of estimated parameteters.
% For any k^2 set of Innovation or AR parameters X,
% reshape(X,k,k) will give the correct matrix
% To recover C, use ivech(parmaeters(1:(k*(k+1))/2)
% loglikelihood - The loglikelihood of the function at the optimum
% Ht - A k x k x t 3 dimension matrix of conditional covariances
% likelihoods - A t by 1 vector of individual likelihoods
% stdresid - A t by k matrix of multivariate standardized residuals
% stderrors - A numParams^2 square matrix of robust Standad Errors(A^(-1)*B*A^(-1)*t^(-1))
% A - The estimated inverse of the non-robust Standard errors
% B - The estimated covariance of teh scores
% scores - A t by numParams matrix of individual scores
%
%
% COMMENTS:
% You should multiply the data by a constant so that the min std(data) is at least 10. This will help estimation
%
%
******************************************************************************* ********
% * THIS FUNCTION INVOLVES ESTIMATING MANY PARAMETERS. THE EXACT NUMBER OF PARAMETERS
% * NEEDING TO BE ESTIMATED IS (k*(k+1))/2+pk^2+qk^2. FOR A 5 VARIATE (1,1) MODEL THIS
% * 65 PARAMETERS. ESTIMATION CAN TAKE A VERY LONG TIME. A 10 ASset MODEL TOOK 12 % * HOURS ON A PIII-700.
%
******************************************************************************* ********
%
%
% Author: Kevin Sheppard
% kevin.sheppard@economics.ox.ac.uk
% Revision: 2 Date: 12/31/2001
% need to try and get some smart startgin values
if size(data,2) > size(data,1)
data=data';
end
[t k]=size(data);
k2=k*(k+1)/2;
scalaropt=optimset('fminunc');
scalaropt=optimset(scalaropt,'TolFun',1e-1,'Display','iter','Diagnostics','on','DiffMaxChange',1e-2) ;
startingparameters=scalar_bekk_mvgarch(data,p,q,scalaropt);
CChol=startingparameters(1:(k*(k+1))/2);
%C=ivech(startingparameters(1:(k*(k+1))/2))*ivech(startingparameters(1:(k*(k+1))/2))';
newA=[];
newB=[];
for i=1:p
newA=[newA diag(ones(k,1))*startingparameters(((k*(k+1))/2)+i)]; %#ok
end
for i=1:q
newB=[newB diag(ones(k,1))*startingparameters(((k*(k+1))/2)+i+p)]; %#ok
end
newA=reshape(newA,k*k*p,1);
newB=reshape(newB,k*k*q,1);
startingparameters=[CChol;newA;newB];
if nargin<=3 || isempty(BEKKoptions)
options=optimset('fminunc');
options.Display='iter';
options.Diagnostics='on';
options.TolX=1e-4;
options.TolFun=1e-4;
options.MaxFunEvals=5000*length(startingparameters);
options.MaxIter=5000*length(startingparameters);
else
options=BEKKoptions;
end
parameters=fminunc('full_bekk_mvgarch_likelihood',startingparameters,options,data,p,q,k,k2,t); [loglikelihood,likelihoods,Ht]=full_bekk_mvgarch_likelihood(parameters,data,p,q,k,k2,t); loglikelihood=-loglikelihood;
likelihoods=-likelihoods;
% Standardized residuals
stdresid=zeros(size(data));
for i=1:t
stdresid(i,:)=data(i,:)*Ht(:,:,i)^(-0.5);
end
%Std Errors
if nargout>=6
A=hessian_2sided('full_bekk_mvgarch_likelihood',parameters,data,p,q,k,k2,t);
h=max(abs(parameters/2),1e-2)*eps^(1/3);
hplus=parameters+h;
hminus=parameters-h;
likelihoodsplus=zeros(t,length(parameters));
likelihoodsminus=zeros(t,length(parameters));
for i=1:length(parameters)
hparameters=parameters;
hparameters(i)=hplus(i);
[HOLDER, indivlike] = full_bekk_mvgarch_likelihood(hparameters,data,p,q,k,k2,t); likelihoodsplus(:,i)=indivlike;
end
for i=1:length(parameters)
hparameters=parameters;
hparameters(i)=hminus(i);
[HOLDER, indivlike] = full_bekk_mvgarch_likelihood(hparameters,data,p,q,k,k2,t); likelihoodsminus(:,i)=indivlike;
end
scores=(likelihoodsplus-likelihoodsminus)./(2*repmat(h',t,1));
B=cov(scores);
A=A/t;
stderrors=A^(-1)*B*A^(-1)*t^(-1);
end
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