GARCH模型在Matlab中的实现

1、多元GARCH模型预测的Matlab程序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. % % % USAGE:% parameters, loglikelihood, Ht, likelihoods, stdresid, stderrors, A, B, sco

2、res = 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*k2+q*k2 vect

3、or of estimated parameteters. F% or any k2 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 covar

4、iances% likelihoods - A t by 1 vector of individual likelihoods% stdresid - A t by k matrix of multivariate standardized residuals% stderrors - A numParams2 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 cova

5、riance of teh scores% scores - A t by numParams matrix of individual scores% need to try and get some smart startgin valuesif size(data,2) > size(data,1) data=data'endt k=size(data);k2=k*(k+1)/2;scalaropt=optimset('fminunc');scalaropt=optimset(scalaropt,'TolFun',1e-1,'Disp

6、lay','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=ne

7、wA diag(ones(k,1)*startingparameters(k*(k+1)/2)+i);endfor i=1:q newB=newB diag(ones(k,1)*startingparameters(k*(k+1)/2)+i+p);endnewA=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.

8、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;endparameters=fminunc('full_bekk_mvgarch_likelihood',startingparamete

9、rs,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 residualsstdresid=zeros(size(data);for i=1:t stdresid(i,:)=data(i,:)*Ht(:,:,i)(-0.5);end%Std Errorsif nargout>=6 A

10、=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