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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Estimating a Log Periodic Power Law model with some constraints
Date   Mon, 22 Mar 2010 14:55:15 -0000

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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