  We perform a comparative study for multiple equity indices of different
countries using different models to determine the best fit using the
Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, the Akaike
information criterion and the Bayesian information criteria as goodness-of-fit
measures. We fit models both to daily and to hourly log-returns. The main
result is the excellent performance of a mixture of three Student's $t$
distributions with the numbers of degrees of freedom fixed a priori (3St). In
addition, we find that the different components of the 3St mixture with
small/moderate/high degree of freedom parameter describe the
extreme/moderate/small log-returns of the studied equity indices.
