  Study of time series data often involves measuring the strength of temporal
dependence, on which statistical properties like consistency and central limit
theorem are built. Historically, various dependence measures have been
proposed. In this note, we first survey some of the most well-used dependence
measures as well as various probability and moment inequalities built upon them
under a high-dimensional triangular array time series setting. We then argue
that this triangular array setting will pose substantially new challenges to
the verification of some dependence conditions. In particular, ``textbook
results" could now be misleading, and hence are recommended to be used with
caution.
