Aggregational Gaussianity And Barely Infinite Variance In Crop Prices
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 unit root, in which case the unconditional variance is infinite. We show 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 characterises the case of Integrated GARCH (IGARCH) processes. Finally, we discuss testing for aggregational Gaussianity under barely infinite varian
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