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    $\begingroup$ The conditional variance of GARCH process is a deterministic in your defined sense, buth the GARCH process is not, since $r_t=\sigma_t\varepsilon_t$, and $\varepsilon_t$ is independent of lags of $t$. $\endgroup$ Commented Nov 20, 2015 at 14:54
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    $\begingroup$ @mpiktas, True. If the GARCH model contains two equations, one for conditional mean (an example of which you wrote above) and the other for conditional variance (which is intuitively, although not mathematically, "the main equation" of the model), my argument only applies to the latter equation. $\endgroup$ Commented Nov 20, 2015 at 15:19