  This paper derives the asymptotic behavior of realized power variation of
pure-jump It\^{o} semimartingales as the sampling frequency within a fixed
interval increases to infinity. We prove convergence in probability and an
associated central limit theorem for the realized power variation as a function
of its power. We apply the limit theorems to propose an efficient adaptive
estimator for the activity of discretely-sampled It\^{o} semimartingale over a
fixed interval.
