Comparison Results for GARCH Processes

15 Pages Posted: 17 Apr 2012

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Franco Pellerey

Polytechnic University of Turin

Carlo Sgarra

Politecnico di Milano- Dipartimento di Matematica

Salimeh Yasaei Sekeh

Ferdowsi University of Mashhad (FUM)

Date Written: April 15, 2012

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.

Keywords: Garch, Convex Order, Peakedness, Kurtosis, Supermodularity

Suggested Citation

Bellini, Fabio and Pellerey, Franco and Sgarra, Carlo and Yasaei Sekeh, Salimeh, Comparison Results for GARCH Processes (April 15, 2012). Available at SSRN: https://ssrn.com/abstract=2040697 or http://dx.doi.org/10.2139/ssrn.2040697

Fabio Bellini (Contact Author)

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Franco Pellerey

Polytechnic University of Turin ( email )

Corso Duca degli Abruzzi, 24
Torino, Torino 10129
Italy

Carlo Sgarra

Politecnico di Milano- Dipartimento di Matematica ( email )

Piazza Leonardo da Vinci
Milan, Milano 20100
Italy

Salimeh Yasaei Sekeh

Ferdowsi University of Mashhad (FUM) ( email )

P.O. Box 91775-1163
Mashhad
Iran

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