Student’s t mixture models for stock indices. A comparative study

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.