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