  We consider the problem of stochastic comparison of general Garch-like
processes, for different parameters and different distributions of the
innovations. We identify several stochastic orders that are propagated from the
innovations to the Garch process itself, and discuss their interpretations. We
focus on the convex order and show that in the case of symmetric innovations it
is also propagated to the cumulated sums of the Garch process. More generally,
we discuss multivariate comparison results related to the multivariate convex
and supermodular order. Finally we discuss ordering with respect to the
parameters in the Garch (1,1) case. Key words: Garch, Convex Order, Peakedness,
Kurtosis, Supermodularity.
