  This paper is concerned with extensions of the classical Mar\v{c}enko-Pastur
law to time series. Specifically, $p$-dimensional linear processes are
considered which are built from innovation vectors with independent,
identically distributed (real- or complex-valued) entries possessing zero mean,
unit variance and finite fourth moments. The coefficient matrices of the linear
process are assumed to be simultaneously diagonalizable. In this setting, the
limiting behavior of the empirical spectral distribution of both sample
covariance and symmetrized sample autocovariance matrices is determined in the
high-dimensional setting $p/n\to c\in (0,\infty)$ for which dimension $p$ and
sample size $n$ diverge to infinity at the same rate. The results extend
existing contributions available in the literature for the covariance case and
are one of the first of their kind for the autocovariance case.
