Maximum likeligood estimatin of GARCH(1,1) model

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Junjun 2012-7-8

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https://ww2.mathworks.cn/matlabcentral/answers/43041-maximum-likeligood-estimatin-of-garch-1-1-model

Hello,

I have a problem in estimating GARCH(1,1) with maximum likelihood method. I hope anyone can help and give me an advice what's wrong with the following code.

%---------------------------------------- % main code with function: garch11.like param = [0.001; 0.001; 0.2; 0.6]; distr = 'normal'; T=1000; data = garch11_sim(param, distr, T);

X = ones(T,1); dataX = [data, X];

k=1; % parameter number in mean equation p=1; q=1;

lowerBounds = []; % Linear inequalities captured, c+p+q

upperBounds = []; % as lower bounds constraints.

SumConA = [-eye(k+1+p+q); ... zeros(1,k+1) ones(1,p) ones(1,q)];

SumConB = [inf;zeros(1+p+q,1); 1];

   options  =  optimset('fmincon');
   options  =  optimset(options , 'TolFun'      , 1e-006);
   options  =  optimset(options , 'Display'     , 'iter');
   options  =  optimset(options , 'Diagnostics' , 'on');
   options  =  optimset(options , 'LargeScale'  , 'off');
   options  =  optimset(options , 'MaxFunEvals' , 400*(2+p+q));

SumConB = SumConB - [zeros(k+1+p+q,1); 1]*2*optimget(options, 'TolCon', 1e-6);

starting = [0.001; 0.0013; 0.2; 0.5];

[parameters, LLF, EXITFLAG, OUTPUT, LAMBDA, GRAD] = fmincon('garch11_like',starting,SumConA,SumConB,[],[],lowerBounds,upperBounds,[],options, dataX, distr);

%----------------------------------------------------

function loglike = garch11_like(param, data, distr)

T = size(data,1); et = data(:,1) - data(:,2:end)*param(1);

ht=zeros(T,1);

ht(1) = param(2)/(1-param(3)-param(4));

for t=2:T; ht(t) = param(2) + param(3)*(et(t-1)^2)+ param(4)*ht(t-1); end

switch distr

    case 'normal'
        loglike0 = -0.5*log(2*pi) - 0.5*(log(ht)) - 0.5*((et.^2)./ht);
        loglike = sum(loglike0);
    case 'tdis'
        v=param(5);
        loglike0 = log(gamma(0.5*(v+1))) - log(gamma(v/2)) - 0.5*log(v*pi*ht) - (v+1)/2*log(1+(et.^2)./(v*ht));
        loglike = sum(loglike0);
end