Abstract: The intention of this research is to understand the behavior of the Cyprus Stock Market. Two time series are used as representatives: the FTSE/CySE 20 and the General index. Both return series are characterized by the presence of heavy tails and reject the Gaussian models. We use a-stable distributions to model the data. Although statistical tests accept the null hypothesis empirical findings of FTSE/CySE 20 show that return distribution takes the shape of a Gaussian distribution at 345 days and the tails appear to become less heavy for less frequent series. Self-similarity is also explored and Hurst exponent is H ? (0:6; 0:65), showing persistent return time series.

Keywords: a-stable distribution, Hurst exponent, heavy tails, infinite variance, Anderson-Darling, Kolmogorov-Smirnov criteria

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