# st: RE: PAC and seasonal differencing

 From "Brian P. Poi" To statalist@hsphsun2.harvard.edu Subject st: RE: PAC and seasonal differencing Date Fri, 20 Feb 2004 14:33:49 -0600

```Earlier today Berhard Hansen (berh@dda.dk) asked:

> I have recently been working with STATA's time series options. The manual
> seems to indicate that a variable can be seasonally differenced in STATA,
> however I can't find the syntax. The first difference is simple enough
> e.g.:   "generate newvariable = D.oldvariable", but what is the code if one
> wants to difference e.g. with respect to the 12th period?

> I have also noticed that when STATA calculates a partial autocorrelation
> function for a series the results differ from the results generated by SPSS
> for the same series. Can anyone explain that?

To create a seasonal difference with a 12-period lag, one can do

. generate seasdiff = oldvariable - L12.oldvariable

The key is the notation L12.oldvariable, which returns the value
from 12 periods ago.

Regarding how the partial autocorrelation function is calculated,
Stata uses a linear regression technique.  Suppose we want the PAC
at lag v for variable x.  Then we run an OLS regression of x on lags
1 through v of x, and the PAC for lag v is the coefficient on the
v-th lag of x.  This method is also mentioned in James Hamilton's
textbook (1993, "Time Series Analysis").

I do not know how SPSS calculates PAC's, but I do know that there are
several different ways to do it.  McCullough (1998, Journal of Economic
and Social Measurement) discussed several different methods, including
least squares methods and a method based on the Yule-Walker equations.
His results suggest that least squares works better than the
Yule-Walker-based method.

Hope this helps.

-- Brian
-- bpoi@stata.com

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```