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Re: st: RE: RE: Estimating a Log Periodic Power Law model with some constraints


From   Steve Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: RE: Estimating a Log Periodic Power Law model with some constraints
Date   Mon, 22 Mar 2010 17:25:54 -0400

I agree  with Nick and Tony's suggestions. For your particular
problem,  you can also re-parameterize:  B -->  ln(1 - exp(bb))   and
z = invlogit(zz).  This might not solve boundary problems because you
require strict inequalities.

For more on inequality constraints see: the FAQ by  Isabel Cañette,
http://www.stata.com/support/faqs/stat/intconst.html

Steve


On Mon, Mar 22, 2010 at 11:28 AM, Lachenbruch, Peter
<Peter.Lachenbruch@oregonstate.edu> wrote:
> From elementary calculus we have that the maximum (or minimum) occurs where the derivative is 0 or on the boundary of the region.  It should be fairly simple to do the nl maximization and check if the solution is interior to the boundary.  If not, there's an easy out (I hope).
>
> Tony
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Monday, March 22, 2010 7:55 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: Estimating a Log Periodic Power Law model with some constraints
>
> We quite often see questions like this and some of the time their
> motivation is very unclear.
>
> Quite often it seems that people are confusing constraints with their
> expectations or hypotheses about parameter values.
>
> Whether that's true here, Stata does not really offer much direct
> support for constraints defined by inequalities.
>
> Why not fit directly? If the constraints are satisfied, there is no
> problem. If not, then the model appears a poor choice for the data --
> or, according to taste, the data are a poor choice for the model.
>
> This may sound a flippant response, but I think this strategy not only
> is simpler but also offers more scope for learning something new.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Mehmet I Canayaz
>
> I am trying to estimate a Log Periodic Power Law model (a simple version
> can be found
> here:http://econophysics.econ.univpm.it/econpapers/abstract/Bree.pdf )
> on some financial data and I am having some difficulties.
>
> The model reads:
>
> P(t) = A +  B  *  (t_c - t) ^ z + C  *  (t_c - t)^z   *  cos ( w *
> ln(t_c - t) - r)
>
> with the following constraints: B<0, 0<z<1.
>
> My first idea was running a nonlinear least squares model on (price)
> P(t) and (time) t with the many coefficients such as A, B, t_c, C etc.
> to be estimated.[t_c is of extreme importance since it shows the time of
> a future burst in a financial bubble]. The problem is: I don't really
> know how to assert the mentioned constraints on nonlinear least squares
> in Stata. Stata doesn't allow me to create a constraint and call it
> like:  nl y x, cons(1)
>
> If you have a better estimation method for this formula or have an idea
> on how to fulfill the constraints I would appreciate your help.
>
>
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>



-- 
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

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