data=Total[#]/Length[#]&@(Import/@FileNames["doc/research/hadamard/data/aging_32_8.000000_16.000000_0.050000_10000000_100000_*.dat"]);

ListLogPlot[data[[;;;;5]]/(32^2),Joined->True,PlotRange->{{0,1000},All}]

rescaledData=MapIndexed[Thread[{Range[0,Length[#1]-1]/(#2[[1]]-1),#1}]&,data/(32^2)];

fit=NonlinearModelFit[
Flatten[Rest/@rescaledData[[20;;-5;;5]],1],
Exp[-(((t/τ))^β)],
{τ,β},t
];

Show[
ListLogPlot[
rescaledData[[10;;-5;;5]],
Joined->True,PlotRange->{{0,100},{0.01,1}},
AxesLabel->{"t / (Subscript[t, 0])","C((Subscript[t, 0]), t)"}
],
LogPlot[fit[t],{t,0,150},PlotStyle->Black]
]

fit["BestFitParameters"]