Model Differences in Log Returns of Stock Prices

Consider differences in log returns for Apple stocks:
Fit a TsallisQGaussianDistribution to the data and compare against the fit with a NormalDistribution:
Compare a histogram of the data to the PDF of the fitted distributions:
Inspect the heavy-tail behavior:
Find the probability that the log difference in price is above $0.10:
Simulate the log difference in price for 30 consecutive days: