GARCH模型在Matlab中的實現(xiàn)

1、多元 GARCH 模型預測的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, scores

2、= 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 vector of estimatedparam

3、eteters. 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 covariances%likelihoods- A t by

4、1 vector of individual likelihoods%stdresid- A t by k matrix of multivariate standardized residuals%stderrors- A numParams2 square matrix of robust StandadErrors(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 nu

5、mParams 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,Display,iter,Diagnostics,on,DiffMaxChange,1e-2);startingparameters=scalar_bekk_

6、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:pnewA=newA diag(ones(k,1)*startingparameters(k*(k+1)/2)+i);endfor i=1:qnewB=newB diag(ones(k,1)*startingparameters(k*(k+1)/2)+i+p);en

7、dnewA=reshape(newA,k*k*p,1);newB=reshape(newB,k*k*q,1);startingparameters=CChol;newA;newB;if nargin=6A=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);like

8、lihoodsminus=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;endfor i=1:length(parameters)hparameters=parameters;hparameters(i)=hminus(i);HOLDER, indivlike = full_bekk_mvgarch_likelihood(hparameters,data,p,q,k,k2,t);likelihoodsminus(