[R] Choosing the optimum lag order of ARIMA model

[Prof Brian Ripley]

On Wed, 5 Sep 2007, Megh Dal wrote:

> Hi Leeds, Thanx for this reply. Actually I did not want to know whether 
> any differentiation is needed or not. My question was that : what is the 
> difference between two models :
>
>  arima(data, c(2,1,2))
>
>  and
>
>  arima(diff(data), c(2,0,2))
>
>  If I am correct then those two models are same. Therefore I should get 
> same results for both of the cases. Am I doing something wrong?

They are not the same.  Please do study the help page, and in particular 
the 'include.mean' argument.  One is a model for n observations and 
the other for n-1 observations, and how that affects the issue is 
discussed on the help page.  With the right options you will get similar 
but not identical results.

> arima(x, c(2,1,2), method="ML")

Coefficients:
          ar1      ar2      ma1     ma2
       0.0786  -0.3561  -0.0869  0.1272
s.e.  0.6135   0.4296   0.6564  0.4549

sigma^2 estimated as 0.01368:  log likelihood = 46.46,  aic = -82.92

> arima(diff(x), c(2,0,2), method="ML", include.mean=FALSE)

Coefficients:
          ar1      ar2      ma1     ma2
       0.0786  -0.3561  -0.0869  0.1272
s.e.  0.6135   0.4296   0.6564  0.4549

sigma^2 estimated as 0.01329:  log likelihood = 47.38,  aic = -82.76


And did you have permission to copy private (and impolite) messages from 
Mr Leeds to this list?  If you did, please say so in your own posting for 
the record.  Since I don't have such permission I have deleted them from 
this reply.

Professor Ripley

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
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