  We propose a new method to construct confidence intervals for quantities that
are associated with a stationary time series, which avoids direct estimation of
the asymptotic variances. Unlike the existing tuning-parameter-dependent
approaches, our method has the attractive convenience of being free of choosing
any user-chosen number or smoothing parameter. The interval is constructed on
the basis of an asymptotically distribution-free self-normalized statistic, in
which the normalizing matrix is computed using recursive estimates. Under mild
conditions, we establish the theoretical validity of our method for a broad
class of statistics that are functionals of the empirical distribution of fixed
or growing dimension. From a practical point of view, our method is
conceptually simple, easy to implement and can be readily used by the
practitioner. Monte-Carlo simulations are conducted to compare the finite
sample performance of the new method with those delivered by the normal
approximation and the block bootstrap approach.
