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The purpose of this article is to investigate whether monthly changes in the General Index of the Athens Stock Exchange contain any nonlinearities. The methodology follows the lead of Brock, Dechert, and Sheinkman statistics (BDS), based on the notion of the correlation integral. The null hypothesis is that the data are independently and identically distributed (iid). This test is applied instead of an attempt to determine if the data are stochastic or chaotic.