Spectral density of an ARMA process
= Spectral density of an ARMA process
{title2=$f_X=\frac{\sigma^2}{\pi}\frac{|\Theta(e^{i\omega})|^2}{|\Phi(e^{i\omega})|^2}$}
With the convention $\Phi(B)X_t=\Theta(B)\varepsilon_t$, the <one-sided spectral density> is $\sigma^2|\Theta(e^{i\omega})|^2/(\pi|\Phi(e^{i\omega})|^2)$ whenever the stationary filter is well defined. Stable autoregressive roots give the causal representation; moving-average invertibility is a separate property.