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

[Mehmet I Canayaz <mehmet@nyu.edu>]

Hi, 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.

Best regards, 

Mehmet Canayaz
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