  In order to calculate the unobserved volatility in conditional
heteroscedastic time series models, the natural recursive approximation is very
often used. Following \cite{StraumannMikosch2006}, we will call the model
\emph{invertible} if this approximation (based on true parameter vector)
converges to the real volatility. Our main results are necessary and sufficient
conditions for invertibility. We will show that the stationary GARCH($p$, $q$)
model is always invertible, but certain types of models, such as EGARCH of
\cite{Nelson1991} and VGARCH of \cite{EngleNg1993} may indeed be
non-invertible. Moreover, we will demonstrate it's possible for the pair (true
volatility, approximation) to have a non-degenerate stationary distribution. In
such cases, the volatility estimate given by the recursive approximation with
the true parameter vector is inconsistent.
