st: Partial autocorrelation (PAC) using Yule-Walker equations

[fjc <fjc120@gmail.com>]

Dear Statalisters:

The Stata 12 manual says that when -corrgram- is used with the yw
option (Yule-Walker equations), the first sample partial
autocorrelation (PAC) is forced to equal the first sample
autocorrelation (AC), as must be true in the population.

I noticed, however, that this is not true when an if condition is used
for the time variable. Here's an example:

. corrgram caemp, lags(12) yw noplot

 LAG       AC       PAC      Q     Prob>Q
-----------------------------------------
1        0.9585   0.9585   127.73  0.0000

. corrgram caemp if tin(1962q1,1993q4), lags(12) yw noplot

 LAG       AC       PAC      Q     Prob>Q
-----------------------------------------
1        0.9492   0.9585   118.05  0.0000

Notice that AC changes but PAC doesn´t.

My if condition leaves 8 observations out (four at the beginning of
the sample, and four at the end). If I drop these observations I get
equality again:

. drop if t<tq(1962q1)
(4 observations deleted)

. drop if t>tq(1993q4)
(4 observations deleted)

. corrgram caemp, lags(12) yw noplot

LAG       AC       PAC      Q      Prob>Q
---------------------------------------------------------
1        0.9492   0.9492   118.05  0.0000

I'm not sure about the reason for this and whether something should be
done about it. Any clarification would be greatly appreciated.

Best,

Francisco.

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