You have
function loglt = lnlt( b,yy)
and
a0=b(1:2);
a1=b(3:4);
b1=b(5:6);
c1=b(7:8);
pp=b(9:10);
where b is the parameters being passed in to be varied. The initial values that were passed in to fminunc for this purpose are in the variable start which is initialized to 3.1 * a where a=[a0 a1 b1 c1 pp]'; and a0=[1.0,1.5]; a1=[0.3,0.5];b1=[0.25,0.2]; c1=[0.65,0.5]; pp=[.2,.6]; .
Now, inside lnlt you have
for i = 2:nobs
hh(i)=a0(s(i))+a1(s(i))*indpositive(v(i-1))*log(v(i-1)^2)+b1(s(i))*indnegative(v(i-1))*log(v(i-1)^2);
h(i)=sqrt(exp((hh(i))))*h(i-1)^c1(s(i));
end
Observe the feedback, that the previous h^c1 is multiplied by a factor. If h becomes greater than 1 and c1 becomes greater than 1, then there is danger of an exponential explosion. With the initial values, c1 is indeed greater than 1, so the question becomes whether the multiplying factor is small enough to dampen the exponential growth. The answer to that is NO, that although some of the hh(i) are negative, so some of the sqrt(exp(hh)) are less than 1, the effect is not nearly enough to counter-act the exponential growth.
You need initial c1 values that involve at least one value less than 1 in order to have a hope in this, so that the sequence has some dampening.
However...
Your code is not suitable for use with fminunc() or fmincon() or any of the mathworks minimizers... including not being suitable for ga() .
All of the MATLAB minimizers rely upon the idea that if you process the same parameters twice, that you will get the same answer. But that is not true for your code: your code calls rando() to determine whether to use the first or second column of numbers, and rando() uses randn(), so your code is not deterministic and so cannot meaningfully be minimized.
