Maximum likelihood Garch with fmincon

Guys,

I am working to create a model Garch with the implementation of another exogenous variable; but I have some problem with the function fmincon

I have a log_lk_GARCH11VIX function with y data.

theta = [0.1;0.3;0.2;0.4];


lb = [0;
      0
      0
      0];
  
ub = [100;
      0.999999
      0.999999
      0.999999];
  %too many input

  [x,fval,exitflag,output,labda,grad,hessian] = fmincon('log_lk_GARCH11VIX',theta,[],[],[],[],lb,ub)

this is the error:

Error using barrier
Objective function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 834)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] =
    barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in esti (line 16)
  [x,fval,exitflag,output,labda,grad,hessian] =
  fmincon('log_lk_GARCH11VIX',theta,[],[],[],[],lb,ub)
 

Answer 1

[Matt J]

Check log_lk_GARCH11VIX(theta). It is returning a bad value.

[Karim Hasouna]

function [log_lik] = log_lk_GARCH11VIX(theta)

global y y11

[T] = size(y,1);

omega = theta(1,1);
alpha = theta(2,1);
beta=theta(3,1);
delta =theta(4,1);

sigma2 = zeros(T,1);
log_likelihood_i = zeros(T,1);

sigma2(1,1) = omega;
log_likelihood_i(1,1) = -0.5 * log(2*pi) - 0.5* log(sigma2(1,1)) - 0.5/sigma2(1,1)*(y(1,1))^2;


for t = 2 : 1 : T
sigma2(t,1) = omega + alpha * y(t-1,1)^2 + beta * sigma2(t-1,1)^2 + delta * y11(t-1,1)^2; 
log_likelihood_i(t,1) = -0.5 * log(2*pi) - 0.5* log(sigma2(t,1)) - 0.5/sigma2(t,1)*(y(t,1))^2;
end

log_lik = -sum(log_likelihood_i);

end

I suppose everything is okay here.

[Karim Hasouna]

I think there is a mistake in the fmincon input/outputs.

I don't know where.

[Matt J]

I suppose everything is okay here.

Why? The error message has told you that the objective function returns a bad value at

theta = [0.1;0.3;0.2;0.4];

Did you check the output when this particular theta is given?