« View all new features in
Mathematica
9
◄
previous

next
►
New in
Mathematica
9
›
Enhanced Probability & Statistics
Model Differences in Log Returns of Stock Prices
Consider differences in log returns for Google stocks.
In[1]:=
X
goog = Differences[ Log[FinancialData["GOOG", {{2008, 3, 10}, {2010, 3, 15}, "Day"}, "Value"]]];
Fit a
TsallisQGaussianDistribution
to the data and compare against the fit with a
NormalDistribution
.
In[2]:=
X
edist1 = EstimatedDistribution[goog, TsallisQGaussianDistribution[\[Mu], \[Beta], q]]
Out[2]=
In[3]:=
X
edist2 = EstimatedDistribution[goog, NormalDistribution[\[Mu], \[Sigma]]]
Out[3]=
In[4]:=
X
DistributionFitTest[goog, #] & /@ {edist1, edist2}
Out[4]=
Compare a histogram of the data to the PDF of the fitted distributions.
In[5]:=
X
h = Histogram[goog, 30, "PDF"]; pdfs = Plot[{PDF[edist1, x], PDF[edist2, x]}, {x, 0.1, .1}, PlotStyle > Thick, PlotLegends > {"Tsallis", "Gaussian"}]; Show[{h, pdfs}, ImageSize > 300]
Out[5]=
Inspect the heavytail behavior.
In[6]:=
X
{QuantilePlot[goog, edist1], QuantilePlot[goog, edist2]}
Out[6]=
Find the probability of the logreturn to exceed 0.10.
In[7]:=
X
Probability[x > 0.1, x \[Distributed] edist1]
Out[7]=
Simulate the log difference in price for 30 consecutive days.
In[8]:=
X
ListLinePlot[RandomVariate[edist1, 30], ImageSize > 300]
Out[8]=