English

Comparison results for Garch processes

Statistical Finance 2012-04-18 v1 Probability Statistics Theory Risk Management Statistics Theory

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 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.

Cite

@article{arxiv.1204.3786,
  title  = {Comparison results for Garch processes},
  author = {Fabio Bellini and Franco Pellerey and Carlo Sgarra and Salimeh Yasaei Sekeh},
  journal= {arXiv preprint arXiv:1204.3786},
  year   = {2012}
}
R2 v1 2026-06-21T20:50:44.947Z