ARMA+GARCH inferred residuals and volatility inconsistency.

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?

Answer 1

[Dimitris Iliou]

If you go the documentation page of the infer function:

http://www.mathworks.com/help/econ/cvm.infer.html

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.