Cross-spectrum Analysis - How the Example Data were Created

Now, let us return to the example data set presented above. The large spectral density estimates for both series, and the cross-amplitude values at frequencies n = 0.0625 and n = .1875 suggest two strong synchronized periodicities in both series at those frequencies. In fact, the two series were created as:

v1 = cos(2*p*.0625*(v0-1)) + .75*sin(2*p*.2*(v0-1))

v2 = cos(2*p*.0625*(v0+2)) + .75*sin(2*p*.2*(v0+2))

(where v0 is the case number). Indeed, the analysis presented in this overview reproduced the periodicity "inserted" into the data very well.