Comparison Results for GARCH Processes
15 Pages Posted: 17 Apr 2012
Date Written: April 15, 2012
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.
Keywords: Garch, Convex Order, Peakedness, Kurtosis, Supermodularity
Suggested Citation: Suggested Citation