Maximum Likelihood Function of GARCH model using "fmincon" function

MUHAMMAD IRFAN MALIK

2016 5 14

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Dear Members, I wants to maximize the likelihood function of my GARCH models using "fmincon" function to compare the resutls of garchfit function of Matlab. I write the following codes for this purpose. The codes are given below.

setting for generation of AR-GARCH series

ModelSpecification = garchset('C',.2,'K',0.2, 'GARCH',0.8,'ARCH',[0.15])

The simulation is done by this command

[e1, s1, r] = garchsim(ModelSpecification, 500,1 );

in above setting "r" is our simulated series with AR_GARCH the program for estimation of garch model is

function y=garchmodel(beta)
load r
n=size(r,1);
residuals=zeros(n,1);
residuals(1,1)=r(1,1)-beta(1,1);
sigma=zeros(n,1);
sigma(1,1)=.000000001;
for i=2:n
    %rr=(r(i-1)-a)^2;
      %sigma(i,1)=c0+c1*rr+c2*sigma(i-1,1);
      %ll=ll+(-log(sigma(i,1)+rr/sigma(i,1)));
      residuals(i,1)=r(i,1)-beta(1,1);
      sigma(i,1)=sqrt(beta(2,1)+beta(3,1)*residuals(i)^2+beta(4,1)*sigma(i-1,1)^2);
  end 
      ll1=-0.5 * ( log(2*pi*(sigma.^2)) + (residuals./sigma).^2 );
y=-sum(ll1);

after we use the "fmincon" function to estimate the parameters of interest by maximization our ll which is "y" with following settings.

function [mn, fv]=minimization1()
beta0=[.0001;.2;.02;0.0];
A  =  [zeros(1,2)  ones(1,1)  ones(1,1)]; 
b  =  .99;
lb=[-100;1e-10;0;0];
ub=[];
%options = struct('MaxFunEvals', 2000);
options=optimset('Algorithm','sqp','MaxFunEvals', 2000,'MaxIter',500,'Diagnostics','on','Hessian','user-supplied');
%opt = optimset('Display','iter');
[mn, fv]=fmincon(@garchmodel,beta0,A,b,[],[],lb,ub,[],options);