Aggregational Gaussianity and Barely Infinite Variance in Financial Returns

22 Pages Posted: 1 Aug 2012

See all articles by Antonios Antypas

Antonios Antypas

University of Piraeus - Department of Banking and Financial Management

Phoebe Koundouri

Athens University of Economics and Business - Department of International and European Economic Studies; University of Reading - Department of Economics

Nikolaos Kourogenis

University of Piraeus, Department of Banking and Financial Management

Date Written: September 28, 2011

Abstract

This paper aims at reconciling two apparently contradictory empirical regularities of financial returns, namely, the fact that the empirical distribution of returns tends to normality as the frequency of observation decreases (aggregational Gaussianity) combined with the fact that the conditional variance of high frequency returns seems to have a (fractional) unit root, in which case the unconditional variance is infinite. We provide evidence that aggregational Gaussianity and infinite variance can coexist, provided that all the moments of the unconditional distribution whose order is less than two exist. The latter characterizes the case of Integrated and Fractionally Integrated GARCH processes. Finally, we discuss testing for aggregational Gaussianity under barely infinite variance. Our empirical motivation derives from commodity prices and stock indices, while our results are relevant for financial returns in general.

Keywords: Aggregational Gausianity, infinite variance, FIGARCH, financial returns

JEL Classification: C10, G12, Q14

Suggested Citation

Antypas, Antonios and Koundouri, Phoebe and Kourogenis, Nikolaos, Aggregational Gaussianity and Barely Infinite Variance in Financial Returns (September 28, 2011). Available at SSRN: https://ssrn.com/abstract=2120104 or http://dx.doi.org/10.2139/ssrn.2120104

Antonios Antypas

University of Piraeus - Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

Phoebe Koundouri

Athens University of Economics and Business - Department of International and European Economic Studies ( email )

GR-10434 Athens
Greece
+0030 210 8203147 (Phone)
+0030 210 8214122 (Fax)

HOME PAGE: http://www.econ.ucl.ac.uk/downloads/koundouri/cv.pdf

University of Reading - Department of Economics ( email )

Reading, RG6 6AA
United Kingdom
+44 - (0)118 - 9875123 (Phone)
+44 - (0)118 - 9750236 (Fax)

HOME PAGE: http://www.rdg.ac.uk/economics/koundouri.html

Nikolaos Kourogenis (Contact Author)

University of Piraeus, Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

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