set >0 constraints on ols estimates: seek alternatives to lsqlin()

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Isma 2015-7-8

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https://ww2.mathworks.cn/matlabcentral/answers/229051-set-0-constraints-on-ols-estimates-seek-alternatives-to-lsqlin

Hi, could someone please advise on the way to set >0 constraints on the following ols estimates (omega, phi_1, tau_1, see below )?

|epsilon_t|^alpha = omega + (phi_1 + tau_1) + |epsilon_t-1|^alpha - phi_1* nu_t-1 + zeta_t;

where nu_t & zeta_t are both error terms.

My matter from the below piece of code (assuming no mistake) is that my estimates are not all >0. Furthermore while using lsqlin() they 're all optimized to zeros which is not helpful.

code:

Epsi = (data - del)/gam;
lagEpsi = [NaN;Epsi(1:end-1)];
signEpsi=sign(Epsi);
Epsi_al=signEpsi.*((signEpsi.* Epsi).^al);
signlagEpsi=sign(lagEpsi);
lagEpsi_al=signlagEpsi.*((signlagEpsi.* lagEpsi).^al);
[b,bint,Resid] = regress(Epsi_al,lagEpsi_al);  % compute and store error term
lagResid=[NaN;Resid(1:end-1)];        % lagged error term
X=[ones(size(Epsi)) lagEpsi_al lagResid];
coeff=regress(Epsi_al, X);