BEKK-GARCH模型之Matlab编程.doc

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*k2+q*k2 vector of estimated parameteters. % For 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 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 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+pk2+qk2. 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.sheppardeconomics.ox.ac.uk% Revision: 2 Date: 12/31/2001% 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_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); %#okendfor i=1:qnewB=newB diag(ones(k,1)*startingparameters(k*(k+1)/2)+i+p); %#okendnewA=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);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;endfor i=1:length(parameters)hparameters=parameters;hparameters(i)=hminus(i);HOLDER, indivlike = full_bekk_mvgarch_likelihood(hparameters,data,p