Perform Spectral Analysis of a Time Series 

Generate a sample path from an ARProcess[1].

In[1]:=

X data = RandomFunction[ARProcess[{.2}, .1], {1, 5000}];

Compute smoothed estimates of the PowerSpectralDensity of the data.

In[2]:=

X Plot[Evaluate@ Table[PowerSpectralDensity[data, \[Omega], i], {i, 5, 20, 5}], {\[Omega], -\[Pi], \[Pi]}, PlotRange -> All, ImageSize -> 300]

Out[2]=

The theoretical PowerSpectralDensity for the ARProcess.

In[3]:=

X Plot[PowerSpectralDensity[ ARProcess[{.2}, .1], \[Omega]], {\[Omega], -\[Pi], \[Pi]}, PlotRange -> All, ImageSize -> 300]

Out[3]=