If the roots of the denominator polynomial are inside the unit circle,
the ACF of the ARMA process, , will go to zero for for some .
Let and be the DFT of and padded to length .
Then the circular power spectrum of size is
The first values of will be accurate approximations to the true ACF.
h = B2./A2;
rho = sig2 * h;
r = real(ifft(rho));
One only needs to increase until the condition is met that
the ACF dies to zero before . See figure 9.2.
Computing ACF with the DFT. Upper panel, too small.
Lower panel large enough.