Do Stock Returns Adhere to the Distribution Stipulated by the Students T-distribution?

When people are analyzing data with thicker tails compared to the normal distribution, students t-distribution is commonly applied, making it potentially relevant in the financial markets, especially returns of a stock. This research focuses on estimating the parameters of the students t-distribution in empirical data, employing the maximum likelihood fitting method in order to determine accurate parameters of estimation. In order to conclude whether the t-distribution is close math or not, we assess the goodness of fit, where synthetic data is generated, and the Kolmogorov-Smirnov (KS) test is applied. Moreover, to determine if the t-distribution is the best fit for the data, a Likelihood ratio test is conducted. It provides a statistical comparison between t-distribution and alternative distributions, allowing us to select the most suitable model. Furthermore, the relationship between volatility and degrees of freedom is examined using a scatterplot. This aims to uncover any potential correlation or patterns between these variables. By undertaking these investigations, we deepened our understanding of the statistical characteristics of stock returns and gained insights for potential applications in financial modeling and risk analysis.