  The goal of this paper is to obtain expectation bounds for the deviation of
large sample autocovariance matrices from their means under weak data
dependence. While the accuracy of covariance matrix estimation corresponding to
independent data has been well understood, much less is known in the case of
dependent data. We make a step towards filling this gap, and establish
deviation bounds that depend only on the parameters controlling the "intrinsic
dimension" of the data up to some logarithmic terms. Our results have immediate
impacts on high dimensional time series analysis, and we apply them to high
dimensional linear VAR($d$) model, vector-valued ARCH model, and a model used
in Banna et al. (2016).
