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The accurate specification of returns distributions has important implications in financial economics. A common practice in financial econometrics is to assume that the logarithms of stock returns are independent and identically distributed and follow a Normal distribution. However, daily stock returns display significant departures from Normality, having fatter tails and more peakedness. This study presents an alternative class of distributions, Levy-stable distributions, which can account for the observed skewness, kurtosis and fat tails, considering a sample of daily returns for nine stocks in Paris Market. Moreover, estimating the Levy-index allows us to determine long-memory behaviour of stock returns. Additionally, this study also tests long-memory hypothesis through an estimation of ARFIMA models. A comparative analysis of both approaches suggests the existence of long-memory in Paris Stock Exchange. The implication of the present work is that Levy-stable distributions are used to better approximate returns distributions and also to explore long-memory effects of stock returns.
