There is a problem I have been trying to solve for a while. Let $X_t$ be a stationary (univariate) time series. The spectral density of the moving average process $$X_t=\sum^{\infty}_{j=-\infty}a_je_{t-j}$$ is $$f_X(\omega)=\frac{\sigma^2}{2\pi}\left(\sum^{\infty}_{j=-\infty}a_je^{-ij\omega}\right)\left(\sum^{\infty}_{j=-\infty}a_je^{ij\omega}\right)$$
Now I want to know how to write $f^{p}_{X}(\omega)$ (square the function for example, i.e. $p=2$). Can someone please give me a hint as to how to do this. Thank you very much in advance.
