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I paper I am trying to replicate used Eviews to estimate their state space model (by maximizing the associated maximum likelihood). They used the BHHH and Marquardt algorithms.

My question is given that the Marquardt algorithm is generally used to solve least square type problems what is Eviews doing to allow it to be applied to maximum likelihood problems?

1.) Does it change the Marquardt algorithm? If so how?

2.) Does it reformulate the log likelihood maximization as a least squares problem? If so how?

Baz

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  • $\begingroup$ It would help if you would cite the paper that you're trying to understand. It would also help to know the form of the likelihood function (which might well be a sum of squares, depending on the details of the model.) $\endgroup$ – Brian Borchers Jul 13 '14 at 22:55
  • $\begingroup$ ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf see p315 for the estimation procedure. $\endgroup$ – Baz Jul 14 '14 at 9:48
  • $\begingroup$ see also here which shows the same model but gives a fuller explanation pure.au.dk/portal-asb-student/files/48326397/… bottom p34 - p38 $\endgroup$ – Baz Jul 14 '14 at 9:49
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If you start with the log likelihood function in (3.19) on page 38 of your second reference (Christensen's MSc thesis in finance), the problem of maximizing the log likelihood becomes a least squares problem. First note that the

$\frac{N}{2} \log 2\pi$

term is constant with respect to $R$, as is the

$\log | F^{-1} |$

term. The remaining

$\frac{1}{2} v_{t} F^{-1} v_{t}$

terms are quadratic, so this is a sum of squares problem. You'll want to switch from maximization to minimization by removing the minus sign.

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  • $\begingroup$ Thanks for this, but I already tried this: the optimizer massively over estimates the variances? $\endgroup$ – Baz Jul 15 '14 at 14:18

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