Comparison Results for GARCH Processes. (30th January 2018)

• Record Type: Journal Article
• Authors: Bellini, Fabio; Pellerey, Franco; Sgarra, Carlo; Yasaei Sekeh, Salimeh
• Is Part Of: Journal of applied probability. Volume 51:Number 3(2014)
• Page Start: 685
• Page End: 698
• Publication Date: 2018-01-30
• Subjects: GARCH, -- convex order, -- peakedness, -- kurtosis, -- supermodularity; 60E15, -- 91G70; 519.2
• DOI: 10.1239/jap/1409932667
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : 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 we 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 orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.