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# Re: st: MA(1) process

 From Robert A Yaffee To statalist@hsphsun2.harvard.edu Subject Re: st: MA(1) process Date Fri, 09 Jul 2010 11:50:15 -0400

```Ari,
If you assume that your mean-centered series is a function of its past observations, it has an AR structure.  AR(1) means that it is a function of
only the first lag of itself.   With an MA(1) structure, the observation is a function of the current and first lag of the disturbance (shock, innovation or error).
You can convert one to the other.  Actually, an AR(1) is functionally equivalent to a MA("infinite") and an AR("infinite") is functionally equivalent to a MA(1), assuming covariance stationarity.
You may first need to test before you make these assumptions.

- Robert

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Ari Dothan <ari.dothan@gmail.com>
Date: Friday, July 9, 2010 11:32 am
Subject: st: MA(1) process
To: statalist@hsphsun2.harvard.edu

> Hi Statalisters,
>  I am using a gmm procedure for dynamic panels which makes it possible
>  to fit a model with an MA(1) error structure (moving average (1st
>  order). Most other procedures, such as fixed effects, use the AR(1)
>  error structure.
>  Could anyone explain me in layman’s terms what is the difference
>  between the MA(1) and the AR(1) error structures? Why, and when,
>  should one be used rather than the other?
>  Thanks
>  --
>  Ari Dothan
>
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```