On the scaling of the distribution of daily price fluctuations in Mexican financial market index

TL;DR

This study analyzes daily log-return fluctuations of the Mexican Stock Market Index over ten years, finding they do not follow a normal distribution but fit an alpha-stable Levy distribution, highlighting the importance of sample size in tail decay estimation.

Contribution

It provides a comprehensive statistical analysis of Mexican stock index fluctuations, emphasizing the distribution fitting and the impact of sample size on tail behavior estimation.

Findings

Normality of fluctuations is rejected.

Log-fluctuations fit an alpha-stable Levy distribution.

Sample size affects tail decay estimation.

Abstract

In this paper, a statistical analysis of log-return fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of daily data covering the period from $04/09/2000-04/09/2010$ was analyzed, and fitted to different distributions. Tests of the goodness of fit were performed in order to quantitatively asses the quality of the estimation. Special attention was paid to the impact of the size of the sample on the estimated decay of the distributions tail. In this study a forceful rejection of normality was obtained. On the other hand, the null hypothesis that the log-fluctuations are fitted to a $\alpha$-stable L\'evy distribution cannot be rejected at 5% significance level.