To better understand the spatial structure of large panels of economic and
financial time series and provide a guideline for constructing semiparametric
models, this paper first considers estimating a large spatial covariance matrix
of the generalized $m$-dependent and $\beta$-mixing time series (with $J$
variables and $T$ observations) by hard thresholding regularization as long as
${{\log J \, \cx^*(\ct)}}/{T} = \Co(1)$ (the former scheme with some time
dependence measure $\cx^*(\ct)$) or $\log J /{T} = \Co(1)$ (the latter scheme
with some upper bounded mixing coefficient).