# Which approach is better to estimate the ARMA model parameters

Started by January 12, 2016
```I have a task to estimate an ARMA system model parameters. The nominator
and denominator orders are known. The ARMA parameters could be estimated
from the time domain or frequency domain through minimizing the
mean-squared error of the measured and the system modeled signals. Which
domain is preferred to estimate the system model?  Note for the frequency
domain, the magnitude of the frequency error is used as an optimization
metric.
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Posted through http://www.DSPRelated.com
```
```On Tue, 12 Jan 2016 18:09:23 -0600, Kathy_pdx wrote:

> I have a task to estimate an ARMA system model parameters. The nominator
> and denominator orders are known. The ARMA parameters could be estimated
> from the time domain or frequency domain through minimizing the
> mean-squared error of the measured and the system modeled signals. Which
> domain is preferred to estimate the system model?  Note for the
> frequency domain, the magnitude of the frequency error is used as an
> optimization metric.

It's going to depend on what you're trying to achieve.  The ARMA
parameter estimation process is essentially an optimization process,
optimization problems give you the answer that you ask for, and the
relationship between what you really want and what you're asking for
isn't always clear.

Just to throw even more fat on your fire, you should be looking not just
at whether to optimize in the time or the frequency domain, but you
should also be looking at whether you want to weight the fit metric more
heavily in some areas or another.

I'd try both domains, and assess the resulting model for fit.  I'd also
try judicious weighting (basically filter both inputs to the ARMA process
with identical filters -- the idea is to emphasize the frequency
components where it counts for your problem, and to de-emphasize them
where it doesn't).

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```On Wednesday, January 13, 2016 at 1:09:28 PM UTC+13, Kathy_pdx wrote:
> I have a task to estimate an ARMA system model parameters. The nominator
> and denominator orders are known. The ARMA parameters could be estimated
> from the time domain or frequency domain through minimizing the
> mean-squared error of the measured and the system modeled signals. Which
> domain is preferred to estimate the system model?  Note for the frequency
> domain, the magnitude of the frequency error is used as an optimization
> metric.
> ---------------------------------------
> Posted through http://www.DSPRelated.com

Recursive least-squares is one solution.
```