We study the spectral behavior of a class of $p$-dimensional stationary linear processes in two different high-dimensional regimes, (A) $p/n \to c \in (0,\infty)$; and (B) $p/n \to 0$, as $p,n \to \infty$. The key structural assumption is that the linear process is driven by a sequence of $p$-dimensional real or complex random vectors with i.i.d. entries possessing zero mean, unit variance and...