Aggregational Gaussianity and barely infinite variance in financial returns |
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| Institution: | 1. Department of Banking and Financial Management, University of Piraeus, Greece;2. Department of International and European Economic Studies, Athens University of Economic and Business, Greece;3. Department of Banking and Financial Management, University of Piraeus, Greece;1. University of Monterrey, Mexico;2. SOAS, University of London, UK;3. ICRE8: International Center for Research on the Environment and the Economy, Greece;4. Athens University of Economics and Business, Greece;5. London School of Economics, UK;6. University of Macedonia, Greece;7. University of Athens, Greece;1. School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China;2. Complex Systems and Network Science Research Center, Southeast University, Nanjing 210096, China;3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China;1. School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China;2. Center of Complex Systems and Network Science Research, Southeast University, Nanjing 210096, China;3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China |
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| 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. |
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