  We establish a Cram\'er-type moderate deviation result for self-normalized
sums of weakly dependent random variables, where the moment requirement is much
weaker than the non-self-normalized counterpart. The range of the moderate
deviation is shown to depend on the moment condition and the degree of
dependence of the underlying processes. We consider two types of
self-normalization: the big-block-small-block scheme and the interlacing or
equal-block scheme. Simulation study shows that the latter can have a better
finite-sample performance. Our result is applied to multiple testing and
construction of simultaneous confidence intervals for high-dimensional time
series mean vectors.
