Student't mixture models for stock indices. A comparative study

TL;DR

This study compares various models for stock index returns and finds that a mixture of three Student's t-distributions best fits the data across different markets and time scales, capturing extreme and moderate returns effectively.

Contribution

It introduces and validates a three-component Student's t mixture model as the most effective fit for stock index returns, outperforming other models in goodness-of-fit measures.

Findings

The 3St mixture model performs best across multiple indices.

Different components of the 3St model capture extreme, moderate, and small returns.

The model is effective for both daily and hourly log-returns.

Abstract

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.