Archivio Istituzionale della RicercaWe consider the problem of stochastic comparison of general GARCH-like processes, for dierent parameters and dierent 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.
Comparison results for GARCH processes / Bellini, F.; Pellerey, Franco; Sgarra, C.; Yasaei Sekeh, S.. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 51:3(2014), pp. 685-698. [10.1239/jap/1409932667]
Comparison results for GARCH processes
PELLEREY, FRANCO;
2014
Abstract
We consider the problem of stochastic comparison of general GARCH-like processes, for dierent parameters and dierent 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.
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https://hdl.handle.net/11583/2513503
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