  The family of U-statistics plays a fundamental role in statistics. This paper
proves a novel exponential inequality for U-statistics under the time series
setting. Explicit mixing conditions are given for guaranteeing fast
convergence, the bound proves to be analogous to the one under independence,
and extension to non-stationary time series is straightforward. The proof
relies on a novel decomposition of U-statistics via exploiting the temporal
correlatedness structure. Such results are of interest in many fields where
high dimensional time series data are present. In particular, applications to
high dimensional time series inference are discussed.
