Journal of Applied Probability

Comparison results for GARCH processes

Fabio Bellini, Franco Pellerey, Carlo Sgarra, and Salimeh Yasaei Sekeh

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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.

Article information

J. Appl. Probab., Volume 51, Number 3 (2014), 685-698.

First available in Project Euclid: 5 September 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91G70: Statistical methods, econometrics

GARCH convex order peakedness kurtosis supermodularity


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.

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