Comparison results for GARCH processes
The goal of the paper is to use various notions of stochastic orderings to systematically compare log-returns modelled by GARCH processes. The authors show how, in general, stochastic orderings (such as increasing, convex and increasing convex order) of the i.i.d. innovations extend to the corresponding stochastic orderings of the log-returns. Under an additional hypothesis on the symmetry of the innovations, convex order is also preserved in the more involved case of the sum of log-returns. A multivariate setting as well as stochastic orderings with respect to the parameters of the process are also considered with similar conclusions.
scientific article; zbMATH DE number 6356253