Hi everybody,<div><br></div><div><div><br></div><div>I am using Kalman filter to esteem a particular financial model. The problem is that Gretl cannot complete the maximum likelihood estimation (see Gretl script below) and report this message:</div>
<div><br></div><div><br></div><div>Sono state usate derivate numeriche</div><div>Tolleranza = 1,81899e-012</div><div>failed to invert OPG matrix GG&#39;</div><div><br></div><div>Errore nell&#39;esecuzione dello script: abbandono</div>
<div>end mle</div><div><br></div></div><div><br></div><div>I cannot understand what is the problem, maybe someone can help me</div><div><br></div><div>Thanks</div><div><br></div><div><br></div><div>Here is the script:</div>
<div><br></div><div><div>matrix y={ENI_Return, ENI_OF, Enel_Return, Enel_OF}</div><div><br></div><div>/* parameter initalization */</div><div><br></div><div>fic = 0.95</div><div>fieni = 0.95</div><div>fienel = 0.95</div><div>
b1r = 0</div><div>b1o = 0</div><div>b2r = 0 </div><div>b2o = 0</div><div>c1r = 0</div><div>c1o = 0</div><div>c2r = 0</div><div>c2o = 0</div><div><br></div><div>/* Kalman filter setup */</div><div><br></div><div>matrix H = {b1r, b1o, b2r, b2o; c1r, c1o, 0, 0; 0, 0, c2r, c2o}</div>
<div>matrix F = {fic, 0, 0; 0, fieni, 0; 0, 0, fienel}</div><div>matrix Q = {1, 0, 0; 0, 1, 0; 0, 0, 1}</div><div>matrix A = {-0.0000015464, 0.20765, 0.000011055, 0.010607}</div><div>matrix R = {0.00000316057284, 0, 0, 0; 0, 68.26394884, 0, 0; 0, 0, 0.00000264875625, 0; 0, 0, 0, 17.57705625}</div>
<div><br></div><div><br></div><div>kalman</div><div>obsy y</div><div>obsymat H</div><div>statemat F</div><div>statevar Q</div><div>obsxmat A</div><div>obsvar R</div><div>end kalman</div><div><br></div><div>/* maximum likelihood estimation */</div>
<div><br></div><div>mle logl = ERR ? NA : $kalman_llt</div><div>    </div><div>H[1,1] = b1r</div><div>H[1,2] = b1o</div><div>H[1,3] = b2r</div><div>H[1,4] = b2o</div><div>H[2,1] = c1r</div><div>H[2,2] = c1o</div><div>H[3,3] = c2r</div>
<div>H[3,4] = c2o</div><div>F[1,1] = fic </div><div>F[2,2] = fieni</div><div>F[3,3] = fienel</div><div><br></div><div>ERR = kfilter()</div><div>params fic fieni fienel b1r b1o b2r b2o c1r c1o c2r c2o</div><div><br></div><div>
end mle</div><div><br></div><div>/* return the smoothed estimate of \Unobsrved variables_t */</div><div><br></div><div>kalman</div><div>obsy y</div><div>obsymat H</div><div>statemat F</div><div>statevar Q</div><div>obsxmat A</div>
<div>obsvar R</div><div>end kalman --diffuse</div><div><br></div><div>series epsilon = ksmooth()</div><br>-- <br>Marcello Bonassoli<br><br>Politecnico di Milano Graduate student<br>
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