ABSTRACT In this paper we investigate the shape of the asset return distribution using all shares index of Helsinki Stock Exchange and Standard & Poor's 500 index of New York Stock Exchange. In both cases the power exponential distribution is used to model the shape of the return distribution and the inference is cross-checked with Student t-distribution. The possible dependencies in the data are studied by pre-whitening it with GARCH techniques and Cochrane-Orcutt correction. The parameters of the power exponential distribution are estimated with Bayesian approach and with maximum likelihood method. Kolmogorov-Smirnov test, for which the critical values are defined with simulation, is used to test the significance of power exponential fit. The results indicate that there are significant variations in the shape of the distribution over time, which cannot be explained by known time-dependencies. This finding suggests that the shape of distribution might be time-dependent or at least it is non-stationary. I...