function F=normstud(theta,e2)
omega=theta(1);
alpha=theta(2);
beta=theta(3);
nu=theta(4);
T=max(size(e2));
s2=zeros(size(e2));
s2(1)=e2(1);
for i=2:T
    s2(i)=omega+alpha*e2(i-1)+beta*s2(i-1);
end

F=-(T-1)*log(Gamma(0.5*(nu+1))/(sqrt(pi*nu)*Gamma(0.5*(nu-2))))+0.5*(nu+1)*sum(log(1+(e2(2:T))./(s2(2:T)*(nu-2))))+0.5*sum(s2(2:T));
