Re: st: SARIMA modeling with 9.0

["Brian P. Poi" <bpoi@stata.com>]

On Sun, 17 Dec 2006, Joe Egger wrote:

> I am new to STATA's ARIMA/SARIMA commands and am trying to fit a SARIMA
> model to a time series of weekly infectious disease incidence, which
> displays a strong 52-week periodicity.
>
> I am using the code:
>
> .arima DS52.incidence, ar(1 3) mar(1/2,52) mma(1/1,52)
>
> which I assume is fitting an AR parameter at lags 1 and 3, seasonal AR
> parameter at lags 1 and 2 and a seasonal MA parameter at lag 1, with the
> series being differenced 2x (1 non-seasonal, 1 seasonal)
>
> When I run this command, STATA has a hard time converging on an
> estimate. I have let it run for 45 minutes but it does not converge.
> Does this model look correct? if so, is the model sufficiently complex
> that estimation just takes this long?
>
> I have aggregated the data to monthly incidence, which makes the command
> the same, except substituting the '52' for '12. when I do this, STATA
> converges on estimates quite quickly (i.e., 20 seconds). Therefore, it
> seems to me the '52' is the problem. any thoughts?
>
> Thanks,
> Joe
Joe,

To carry out the Kalman filter recursions which are used to evaluate the 
likelihood function, -arima- must invert a matrix whose size depends on 
the square of the longest AR or MA term in the model.  With even just one 
period-52 seasonal AR term, that matrix will have about 3000 columns, and 
inverting a 3000x3000 matrix is slow.  During the optimization process, 
-arima- must invert a matrix of that size many times.  If you add a second 
seasonal AR or MA term, the matrix has well over 10,000 columns.

What you can do is try the "diffuse" option.  That avoids the need to 
invert such a large matrix.  If your series is reasonably long and doesn't 
have a long memory, then the results will be very similar to those you 
would obtain without using the diffuse prior for starting the Kalman 
recursions.

Hope this helps.

   -- Brian Poi
   -- bpoi@stata.com
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