## How Does AUTOREG Interpolate When Missing Values?

I have the following time series.

``````data have;
do i=1 to 50;
if i=25 then x=.;
else x=rannor(1);
output;
end;
run;``````

So the 25th observation is missing. When AUTOREG estimates GARCH as follows,

``````proc autoreg noprint;
model x=/garch=(q=1,p=1,type=exp);
output ht=h out=have;
run;``````

SAS computes the 26th conditional variance despite the missing in 25. How can SAS compute h(26) without e(25)? I am reading the AUTOREG manual but couldn't find the answer yet.

P.S. How does AUTOREG compute the EGARCH unconditional variance? There is no reference in the manual.

## Re: How Does AUTOREG Interpolate When Missing Values?

This question has been answered via Technical Support track and below is a summary of the answer to this question:

For computation of conditional error variance for EGARCH model, it is based on the following formula:

ln(ht)=ω+qi=1αig(zti)+pj=1γjln(htj)

When lagged g(z_t-i) is not available due to missing values in the data, the second term in the above formula is set to zero.

For computation of unconditional variance, it is set to missing for EGARCH model since you cannot compute E(h_t) based on

E(ln(h_t)).

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