Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 3 (2014), 685-698.
Comparison results for GARCH processes
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.
J. Appl. Probab., Volume 51, Number 3 (2014), 685-698.
First available in Project Euclid: 5 September 2014
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Bellini, Fabio; Pellerey, Franco; Sgarra, Carlo; Yasaei Sekeh, Salimeh. Comparison results for GARCH processes. J. Appl. Probab. 51 (2014), no. 3, 685--698. doi:10.1239/jap/1409932667. https://projecteuclid.org/euclid.jap/1409932667