当前位置:文档之家› BEKK-GARCH模型之Matlab编程

BEKK-GARCH模型之Matlab编程

BEKK-GARCH模型之Matlab编程
BEKK-GARCH模型之Matlab编程

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@https://www.doczj.com/doc/804785607.html,

% 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

相关主题
相关文档 最新文档