How can I write Matlab code for NGARCH Model?

[Chloe Lin]

I tried to write a code to estimate the variables for NGARCH model:
\(\sigma(t+1)^2=\omega+\alpha*(Return(t)-\theta*\sigma(t))^2+\beta*\sigma(t)^2\) where \(\omega=\sigma*(1-\alpha*(1+\theta^2)-\beta)\)
I wrote a function as

function f=osllh(x)
r=xlsread('HW_3_Data','old vix','j4:j1257');
ovix=xlsread('HW_3_Data','old vix','f4:f1257');
sigma=var(r);
omega=sigma*(1-x(1)*(1+x(3)^2)-x(2));
llh=zeros(1254,1);
for n=1:1254
    opsigma=ones(1254,1);
    opsigma(1,1)=sigma;
    for t=1:1253
        opsigma(t+1,1)=omega+x(1)*(r(t,1)-x(3)*opsigma(t,1)^0.5)^2+x(2)*opsigma(t,1)+x(4)*ovix(t,1)^2/252;
    end
    ollh(n,1)=-0.5*log(2*3.1415926)-0.5*log(opsigma(n,1))-0.5*(r(n,1)^2/opsigma(n,1));   
end
    f=-sum(ollh);
end

then use fmincon to call it. But seems that it doesn't converge. The matlab just keep searching and searching and never stops.

Anyone can give me some advice?

Thank you

 

[Andy Nguyen]

First, the code in your .m file is not correct. You need to use ollh consistently throughout the function. I assume osllh, llh are typos and should be ollh. If they are other function calls, you need to post the function body.
Second, you need to attach the HW_3_data.xls for people to be able to test this ollh function. Without it, there isn't much people can help.

 

[Chloe Lin]

Sorry. I'll just repost the code with the data file attached.

[x,fval]=fmincon(@ollh,x0,[],[],[],[],[],[],@mycon)

function f=ollh(x)
r=xlsread('HW_3_Data','old vix','j4:j1257');
ovix=xlsread('HW_3_Data','old vix','f4:f1257');
sigma=var(r);
omega=sigma*(1-x(1)*(1+x(3)^2)-x(2));
llh=zeros(1254,1);
for n=1:1254
    opsigma=ones(1254,1);
    opsigma(1,1)=sigma;
    for t=1:1253
        opsigma(t+1,1)=omega+x(1)*(r(t,1)-x(3)*opsigma(t,1)^0.5)^2+x(2)*opsigma(t,1)+x(4)*ovix(t,1)^2/252;
    end
    ollh(n,1)=-0.5*log(2*3.1415926)-0.5*log(opsigma(n,1))-0.5*(r(n,1)^2/opsigma(n,1));   
end
    f=-sum(ollh);
end

About the constraint function:

function [c,ceq]=mycon(x)
c(1)=x(1)*(1+x(3)^2)+x(2)-1;
ceq=[]
end

Thank you!