# what justify an AR model?

Started by August 16, 2007
```If a time series is supposed to be generated by an AR model, how to
justify such a supposition, what's the physical mechanism behind it?
that is, why not model it by a MA or ARMA model?
Is Yule-Walker the common and PRACTICAL way to find out the parameters
of the AR model?
Pls give some light on this.

```
```On 16 Aug, 08:38, zqchen <zhiqun.c...@gmail.com> wrote:
> If a time series is supposed to be generated by an AR model, how to
> justify such a supposition, what's the physical mechanism behind it?
> that is, why not model it by a MA or ARMA model?

Answering those questions constitute the "art" part of
"The Art of Data Analysis."

> Is Yule-Walker the common and PRACTICAL way to find out the parameters
> of the AR model?

The AR model is certainly one of the less complicated
models, from a purely practical point of view. You find
the same sort of reasoning several places:

- Gaussian mstochastic odels are used because they only
require 2nd order statistics; all other models require
higher order statistics for analysis.

- Linear models are proular because they can easily
be analyzed and solved, note because they are "true"
in a philosophical sense.

Rune

```
```On Aug 16, 6:38 pm, zqchen <zhiqun.c...@gmail.com> wrote:
> If a time series is supposed to be generated by an AR model, how to
> justify such a supposition, what's the physical mechanism behind it?
> that is, why not model it by a MA or ARMA model?
> Is Yule-Walker the common and PRACTICAL way to find out the parameters
> of the AR model?
> Pls give some light on this.

You can of course. An ARMA model normally needs access to the driving
signal though methods such as extended least-squares or recursive ML
can make approximations to innovations models. With an AR model it
would need to be higher order than an ARMA and for some applications
(say speech synthesis) an AR model would have trouble with nasal
sounds. As for a pure MA model - that too could be used but would need
to be even bigger than the all-pole version.

```
```On Aug 16, 2:38 am, zqchen <zhiqun.c...@gmail.com> wrote:
> If a time series is supposed to be generated by an AR model, how to
> justify such a supposition, what's the physical mechanism behind it?
> that is, why not model it by a MA or ARMA model?
> Is Yule-Walker the common and PRACTICAL way to find out the parameters
> of the AR model?
> Pls give some light on this.

i dunno, but i always thought the justification or motivation for the
model has something to do with Markov processes, which essentially
imply that there is some self-similarity in the states of the model in
time.  that what the states are at time n will be similar to what the
states were at times n-1, n-2, etc.  the parameters are the coupling
constants for how similar the present is to each of those times, n-1,
n-2, etc.

sorta like modeling a drunk's walk or something  where the drunk is at
time n will likely be more coupled to where she was at times n-1, n-2,
than where she was n-(1 day).

r b-j

```