ARMA modeling

I am looking for an algorithm to model a system using an ARMA filter. The 
input and the desired output are available. Is there an iterative algorithm 
that can give a global optimum solution ? Any good reference ?

Regards

Tom 

On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom


Simon Haykin, "Adaptive Filter Theory"

On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom


And oh, it might be useful to define what you mean by a "global
optimum solution" (a.k.a, your optimization criteria).

On Jun 13, 1:21 pm, BERT <callm...@gmail.com> wrote:
> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> And oh, it might be useful to define what you mean by a "global
> optimum solution" (a.k.a, your optimization criteria).

And if the original poster defines what he means by "iterative".
Is it iterative in the samples received, or in terms of solving
what this "global optimum solution" is?

On Wed, 13 Jun 2007 18:56:26 -0000, julius <juliusk@gmail.com> wrote:

>On Jun 13, 1:21 pm, BERT <callm...@gmail.com> wrote:
>> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>>
>> > I am looking for an algorithm to model a system using an ARMA filter. The
>> > input and the desired output are available. Is there an iterative algorithm
>> > that can give a global optimum solution ? Any good reference ?
>>
>> > Regards
>>
>> > Tom
>>
>> And oh, it might be useful to define what you mean by a "global
>> optimum solution" (a.k.a, your optimization criteria).
>
>And if the original poster defines what he means by "iterative".
>Is it iterative in the samples received, or in terms of solving
>what this "global optimum solution" is?

Yeah, Parks-McLellan is iterative, but it only takes care of the "MA"
part of ARMA.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Any optimization criteria is OK as long as  the solution is optimal 
(unique). In addition samples are available, iterative or non-iterative both 
are ok.

Thanks

Tom
"BERT" <callmevc@gmail.com> wrote in message 
news:1181758907.555174.71980@i38g2000prf.googlegroups.com...
> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>> I am looking for an algorithm to model a system using an ARMA filter. The
>> input and the desired output are available. Is there an iterative 
>> algorithm
>> that can give a global optimum solution ? Any good reference ?
>>
>> Regards
>>
>> Tom
>
>
> And oh, it might be useful to define what you mean by a "global
> optimum solution" (a.k.a, your optimization criteria).
> 

On Jun 13, 2:19 pm, BERT <callm...@gmail.com> wrote:
> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> Simon Haykin, "Adaptive Filter Theory"

I wouldn't recommend that book for ARMA modeling; there isn't much any
information on that technique in the text. Haykin (rightfully) points
out that ARMA modeling is in general a nonlinear problem, which is
much more difficult to produce than a model with a simpler AR
structure.

On the other hand, it is, IMO, a great adaptive filtering text.

Jason

On Jun 14, 6:19 am, BERT <callm...@gmail.com> wrote:
> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> Simon Haykin, "Adaptive Filter Theory"

I don't think that book will help him much. A better book is Ljung and
Sodestrom Theory and Practice of Recursive Estimation, MIT Press 1983.

On Jun 13, 10:53 am, "Tom" <tomda...@yahoo.com> wrote:
> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom

You could be more clear about what you want.  A quick solution or in
depth knowledge.  I use a minimizing or optimizing algorithm.  These
exist in Scilab as lsqrsolve and optim.  In Mathcad I use Minerr.  In
C I use lmfit.c which is c code converted from ancient fortran but it
works.  There are other versions out there that are buggy.

If iterative means on-the-fly there is the recursive least squares
method but I would be careful with this.  In my testing, a fast sample
rate yields poles close to the unit circle.  The poles move around a
bit while updating and sometimes the poles would cross the unit
circle.  Not good.

What ever method you chose you must make a decision as to how many
coefficients you need.  One can always get a smaller norm or mean
squared error by adding more coefficients but often the poles in the z
domain end up on the negative real axis which is an indicator that you
probably have too many coefficients.  I don't use the recursive least
squares but I do find it interesting how the poles move around and by
how much.

I read about the Levenberg-Marquardt algorithm in Numerical Recipes in
C but didn't like the code or the restrictions.  After that I found
tracing through lmfit.c code helpful.  I didn't need anything beyond
this.

Peter Nachtwey

If you are looking for Levenburg-Marquardt, I would suggest levmar.

http://www.ics.forth.gr/~lourakis/levmar/

You will need the BLAS 1 and LAPACK libraries.  I think the code from ATLAS is 
the best choice.

In article <1182034526.765823.116870@x35g2000prf.googlegroups.com>, 
pnachtwey@gmail.com wrote:
>On Jun 13, 10:53 am, "Tom" <tomda...@yahoo.com> wrote:
>> I am looking for an algorithm to model a system using an ARMA filter. The
>> input and the desired output are available. Is there an iterative algorithm
>> that can give a global optimum solution ? Any good reference ?
>>
>> Regards
>>
>> Tom
>
>You could be more clear about what you want.  A quick solution or in
>depth knowledge.  I use a minimizing or optimizing algorithm.  These
>exist in Scilab as lsqrsolve and optim.  In Mathcad I use Minerr.  In
>C I use lmfit.c which is c code converted from ancient fortran but it
>works.  There are other versions out there that are buggy.
>
>If iterative means on-the-fly there is the recursive least squares
>method but I would be careful with this.  In my testing, a fast sample
>rate yields poles close to the unit circle.  The poles move around a
>bit while updating and sometimes the poles would cross the unit
>circle.  Not good.
>
>What ever method you chose you must make a decision as to how many
>coefficients you need.  One can always get a smaller norm or mean
>squared error by adding more coefficients but often the poles in the z
>domain end up on the negative real axis which is an indicator that you
>probably have too many coefficients.  I don't use the recursive least
>squares but I do find it interesting how the poles move around and by
>how much.
>
>I read about the Levenberg-Marquardt algorithm in Numerical Recipes in
>C but didn't like the code or the restrictions.  After that I found
>tracing through lmfit.c code helpful.  I didn't need anything beyond
>this.
>
>Peter Nachtwey
>