On Fri, 16 Feb 2018, Alecos Papadopoulos wrote: There are two reemarks I'd like to make here: one is related to the syntax of the mle line. In your example, "q" is the full matrix of observations, but "qform(q, inv(S))" implicitly refers to q as the i-th row of that matrix. A minimal modification of your script that fixes this is <hansl> nulldata 128 series N1 = normal() series N2 = normal() scalar s1 = 1 scalar s2 = 1 scalar c12 = 0.5 matrix q = {N1, N2} mle logl = check ? -0.5 * (qqq + ldet(S)) : NA matrix S = {s1^2,c12;c12,s2^2} scalar check = (s1>0) && (s2>0) && (abs(c12)<1) matrix qq = q * inv(S) series qqq = sumr(q.*qq) params s1 s2 c12 end mle # check Shat = q'q ./ $nobs print Shat eval sqrt(diag(Shat)) </hansl> Having said this, though, there's a more general point, on the check for positive definiteness of S. If you reparametrise the problem, you can make S pd by construction simply optimising over the elements of the Cholesky factor of S rather than S itself. This is a very nice trick, which saves you lots of intermediate computation, works quite well in practice and is trivial to generalise to any number of columns of q. For example: <hansl> nulldata 128 series N1 = normal() series N2 = normal() scalar s1 = 1 scalar s2 = 1 scalar c12 = 0.5 matrix q = {N1, N2} matrix S = I(2) matrix theta = vech(S) mle logl = -0.5 * (qqq + ldet(S)) matrix K = lower(unvech(theta)) matrix S = K*K' matrix qq = q * invpd(S) series qqq = sumr(q.*qq) params theta end mle # check Shat = q'q ./ $nobs eval cholesky(Shat) </hansl> Hope this helps. ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------