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Model Differences in Log Returns of Stock Prices

Consider differences in log returns for Apple stocks:
Wolfram Language code: apple = Differences[Log[FinancialData["AAPL", {{2008, 3, 10}, {2010, 3, 15}, "Day"}, "Value"]]];
Fit a TsallisQGaussianDistribution to the data and compare against the fit with a NormalDistribution:
Wolfram Language code: edist1 = EstimatedDistribution[apple, TsallisQGaussianDistribution[μ, β, q]]
Wolfram Language code: edist2 = EstimatedDistribution[apple, NormalDistribution[μ, σ]]
Wolfram Language code: DistributionFitTest[apple, #]& /@ {edist1, edist2}
Compare a histogram of the data to the PDF of the fitted distributions:
Wolfram Language code: h = Histogram[apple, 30, "PDF"]; pdfs = Plot[{PDF[edist1, x], PDF[edist2, x]}, {x, -0.1, .1}, PlotStyle -> Thick, PlotLegends -> {"Tsallis", "Gaussian"}]; Show[{h, pdfs}, ImageSize -> 300]
Inspect the heavy-tail behavior:
Wolfram Language code: {QuantilePlot[apple, edist1], QuantilePlot[apple, edist2]}
Find the probability that the log difference in price is above $0.10:
Wolfram Language code: Probability[x > 0.1, xedist1]
Simulate the log difference in price for 30 consecutive days:
Wolfram Language code: ListLinePlot[RandomVariate[edist1, 30], ImageSize -> 300]