What Unconditional Variance Does AUTOREG Use?

[Junyong]

The following code (1) downloads McDonald's stock prices from July 5, 1966 to November 1, 2021, (2) computes its percent returns, and (3) estimates the GARCH(1,1) model.

filename mcd url 'https://query1.finance.yahoo.com/v7/finance/download/
mcd?period1=-999999999&period2=9999999999';

proc import file=mcd dbms=csv replace out=mcd;
run;

proc expand out=mcd;
	id date;
	convert adj_close=return/tout=(pctdif);
run;

proc autoreg;
	model return=/garch=(q=1,p=1);
	output ht=variance out=mcd;
run;

Because ARCH1+GARCH1=0.0485+0.9539=1.0024>1, the unconditional variance is undefined. However, the output data set assigns 3.8592488163 as the variance of the first observation—how does AUTOREG compute this value of 3.8592488163 here? It seems this is not documented in The AUTOREG Procedure.

[Ksharp · Accepted solution]

It would be better if you post it at Forecasting forum,since it is about SAS/ETS