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Time Series and Stochastic Differential Equations
Simulate Time Series Data
Any time series process in
Mathematica
can be used to simulate random time series data. Use
ARProcess
,
MAProcess
, or
ARMAProcess
to simulate a weakly stationary time series.
In[1]:=
X
RandomFunction[ARMAProcess[{.1, .2}, {.3, .2}, 1], {0, 250}]; ListPlot[%, Filling > Axis]
Out[1]=
Use
ARIMAProcess
to simulate a time series with a trend.
In[2]:=
X
RandomFunction[ARIMAProcess[{.7}, 2, {.2}, 1], {0, 250}]; ListPlot[%, Filling > Axis]
Out[2]=
Use
SARMAProcess
or
SARIMAProcess
to simulate seasonal time series.
In[3]:=
X
RandomFunction[ SARIMAProcess[{.4}, 1, {1.3}, {12, {.7, .3}, 2, {.7, .3}}, 1], {0, 250}]; ListPlot[%, Filling > Axis]
Out[3]=
Use
FARIMAProcess
to simulate a long memory time series.
In[4]:=
X
RandomFunction[FARIMAProcess[{.1}, .45, {.2}, 1], {0, 250}]; ListPlot[%, Filling > Axis]
Out[4]=