nonlinear simultaneous equations nlsur for each observation

[Aurora13]

Hi, everyone!
I'm trying to solve the simultaneous system of two equation to get the daily data of variables va and siga (given the initial values va_init and siga_init).
a = {va} * normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga}) -c* exp(-(b))* normal(((log({va}/c)+(d+0.5*({siga}^2)))/ {siga})-{siga})
d = ({va}/a)* normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga})*{siga}

I'm using -nlsur in stata to get them, but for some reason the formula cannot calculate these value for each observation (which is needed here), but only for the group.

Here is the formula I use:
nlsur (a = {va} * normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga}) -c* exp(-(b))* normal(((log({va}/c)+(d+0.5*({siga}^2)))/ {siga})-{siga})) (d = ({va}/a)* normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga})*{siga}), initial(va va_init[_n] siga siga_init[_n])


If I try to calculate it the following way:
by one, sort: nlsur (a = {va} * normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga}) -c* exp(-(b))* normal(((log({va}/c)+(d+0.5*({siga}^2)))/ {siga})-{siga})) (d = ({va}/a)* normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga})*{siga}), initial(va va_init[_n] siga siga_init[_n])
--> I get the error: cannot have fewer observations than parameters

But this is exactly what I need to calculate:
Does anyone know the solution for my problem?

I also attach the example file, so that you can try it.

[Jorge Eduardo Perez Perez]

nlsur is an estimation command, with the syntax you provide it will give you a single value of va and siga for the whole model. It is not a simultaenous equation solver. I wonder why you thought of nlsur to address this problem.
From the syntax, the value of siga and va for each observation seems to depend on other variables only. I suppose there isn't a closed form solution for the system and that's why you tried this.

Have you seen this FAQ?

http://www.stata.com/support/faqs/pr...ear-equations/

[Aurora13]

nlsur is an estimation command, with the syntax you provide it will give you a single value of va and siga for the whole model. It is not a simultaenous equation solver. I wonder why you thought of nlsur to address this problem.
From the syntax, the value of siga and va for each observation seems to depend on other variables only. I suppose there isn't a closed form solution for the system and that's why you tried this.

Have you seen this FAQ?

http://www.stata.com/support/faqs/pr...ear-equations/

Hi Jorge Eduardo Pérez Pérez,
thank you for the reply.

Yes, I saw this FAQ about nl. So you think nl will be a better choice of the command for this kind of model?

I tried
nl (y= (a - {va} * normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga}) +c* exp(-(b))* normal(((log({va}/c)+(d+0.5*({siga}^2)))/ {siga})-{siga}))^2 + (d - ({va}/a)* normal((log({va}/c)+(b+0.5*({siga}^2)))/ {siga})*{siga})^2)
where y is the vector of zeroes, but the result is the same:
in this case I get the error "y has zero variance", and for one observation - cannot have fewer observations than parameters....

[Jorge Eduardo Perez Perez]

Yes, I saw this FAQ about nl. So you think nl will be a better choice of the command for this kind of model?

Yes, according to the FAQ nl is the way to go here.

in this case I get the error "y has zero variance"

The FAQ states that you have to create y as to have the value 1 in the first observation. Did you do that? Otherwise y will have zero variance and the command will fail.

[Aurora13]

Yes, according to the FAQ nl is the way to go here.

The FAQ states that you have to create y as to have the value 1 in the first observation. Did you do that? Otherwise y will have zero variance and the command will fail.

Hi, I changed y for the value1 in the first observation, but unfortunately the initial problem remained the same:
It still gives only the single va and siga for the model, while I need distinct values for each observation...

[Tom Jefferson]

Are you trying to solve a system of two equations for two unknowns? In that case, rather than playing tricks with -nl- or -nlsur-, you might want to consider using the -solvenl- function in Mata assuming you have Stata 13. It's designed specifically for what you want to do. Type

help solvenl


Tom