Here's my first try to calculate a Cross Periodogram with Gretl. It's obviously not perfect, but I think it is a bit useful. Maybe someone feels adressed to continue the development for a cross spectral density or something else ...the values are (nearly) the same as with Statistica.

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nulldata 200
#generate two related processes

series  X=0
series  Y=0
X=0.9*X(-1)+normal()

Y= 0.4*X + 0.75*Y(-1)+normal()


X1={ X }
Y1={ Y }
Fx=fft(X1)
Fy=fft(Y1)

#lambda = seq(1,($nobs/2))'.*(1/$nobs)

series a=Fx[,1]
series b=Fx[,2]

series c=Fy[,1]
series d=Fy[,2]

#Computes the cross-periodogram with x as a dependent
series crossxy_re=(a*c+b*d)/($nobs/2)
series crossxy_im=(b*c-a*d)/($nobs/2)

#Computes the cross-periodogram with y as a denpendent (imaginary part - the real part is the same as with x as a dependent)
series crossyx_im=(d*a-c*b)/($nobs/2)


delete a b c d

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Kind regards

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