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Random Processes
Estimate Process Parameters from Data
In[1]:=
X
stock = \!\(\* TagBox[ RowBox[{"TemporalData", "[", PanelBox["1", FrameMargins>Small], "]"}], InterpretTemplate[TemporalData[Automatic, {CompressedData[" 1:eJwUV3k4lG8Xtu/L2MfYzTDGliX7MqcQLYokRZEWIkQhSSVEKUTZIlooSkoq RT9zokVlSShRSWTLLkvW7/3+mOu93nne5znnOec+59y3yt7DWw9wsLGxsRO/ dSJsbKaGuxwb/7azDsw/fF54rZ1lCtpvKzf3sM7lKomUH/jNGmTLmaksmWT9 W5Ddx7d6imXf9VzhSMAsK8h/54E/PtOsYBszPznmFMt/jZO36+s/rFIbo03h bd9ZQTKyyjzj9axb/AZvo+R7mOwnljrWZU8zb90zFy/1ZAMLgck93BfZIfyc RtWzODZ4H+ezs2RymVk0XfJjQXWB2X+xKLVDaZb5u/6OfNzwHDMn7YhWTuAs 83ycQ+DdHf+YwmmXzL+p/WMGnnNWjv40y6Tdil8arZlkxtoe0DN0nGDOMPL3 pTZOMOUjHEjhklPMYcohqlFWL7PBUto6svQR0/vRIRmTj9Us24DVoo4+bSxt WVZPx/km1tbJI5L2St2sunfMwuXwX6yOcxQRr4+trBt8ZlerIp6zDCcvJwz7 f2DaeB9aVh36yux3esLHEfObeUPAnu2GxjhT+9HuZP3BOeYx08ea63bPMPfE hB7dwzfHlFC0ufBjywJTfGL025OAf8w7LDfJ1Ow5prYe+ztIn2VWbSh+02Q0 yzy7dt4wb+gv0/qNHnui5wQzS+/EmM3ZCWa/ct3LnXf/MEUKJXsUT3QxNfe2 H6intbJkprZHuN5vZZEeX73rG9PDotPeJcdEDrAYGQ3fHBr7WNMp8++4rLtZ 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In[2]:=
X
Labeled[DateListPlot[stock["Path"], PlotStyle > Thick, ImageSize > 400, Joined > True, Filling > 30], Column[{Style["Simulated Daily Returns", Bold, FontSize > 18, FontFamily > "Helvetica"], Style["1995 to 2005", Bold, FontSize > 16, FontColor > Gray, FontFamily > "Helvetica"]}], {{Top, Left}}]
The following data is daily returns for a hypothetical stock simulated from a
FractionalBrownianMotionProcess
from January 1995 to January 2005.
Out[2]=
The estimated Hurst exponent suggests a long memory process.
In[3]:=
X
pars = FindProcessParameters[stock, FractionalBrownianMotionProcess[h]]
Out[3]=
This is exemplified by the
CorrelationFunction
of the estimated process.
In[4]:=
X
ListPlot[Table[ CorrelationFunction[FractionalBrownianMotionProcess[h] /. pars, 1, j], {j, 100}], Filling > Axis, PlotRange > All]
Out[4]=