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ARMA+GARCH inferred residuals and volatility inconsistency.

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I am puzzled why I am getting two different values from the same data, but different lengths. The residuals of the model match up however the conditional variances is not.
rng(1);
y=randn(100,1)
y=.01+cumsum(y)*.0025;
mdl=arima(3,0,3);
mdl.Variance=garch(1,1);
mdl=estimate(mdl,y);
[residuals,lo] = infer(mdl,y);
ret=y(1:10);
[E,LV]=infer(mdl,ret);
LV-lo(1:10);
(E-residuals(1:10))==0 %<----zero as expected
(LV-lo(1:10))==0 %<----this should be zero as well
Can someone help me understand why the conditional variances are not the same?

Answers (1)

Dimitris Iliou
Dimitris Iliou on 14 Jul 2017
If you go the documentation page of the infer function:
you will notice the following on the description:
" infer(Mdl,Y) infers the conditional variances of the fully specified, univariate conditional variance model Mdl fit to the response data Y "
When your data Y has different number of points, I believe that the conditional variances might be a bit different because of the fitting. That is why you noticed that small difference in the values.

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