Re: st: Why does Stata estimate different partial autocorrelations?

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

On Tue, 15 Feb 2005, Gewei Wang wrote:

> Hi, all,
>
> I just found the Stata's command -- corrgram -- gives different results
> of partial autocorrelations from other statistical softwares such as SAS
> and Eviews. Of course, the -- pac -- creates different plots. In
> particular, Stata's one period lag partial autocorrelation is different
> with one period lag autocorrelation. However, other softwares report
> same values. Who can tell me the reason? Thanks a lot.
>
> Gewei

Gewei,

There are several different ways that the partial autocorrelation
funtion can be calculated.  Stata's -pac- and -corrgram- commands use
a linear regression-based technique; see the Methods and Formulas in
[TS] corrgram for details.

Another way of computing the PAC's is to use the Yule-Walker equations,
and the other software packages you mentioned may be doing that. The
Yule-Walker equations are discussed in many time-series books, including
Box, Jenkins, and Reinsel's "Time Series Analysis: Forecasting and 
Control".

The Yule-Walker method will result in the first PAC being equal to the
first AC (as is true in the population), but the linear regression method
Stata uses will not.  On the other hand, the Yule-Walker method does not
work very well when the series is close to being nonstationary.

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 Poi
  -- StataCorp LP
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