Suppose we observe a uniformly ergodic Markov chain with unknown trans
ition distribution. The empirical estimator for a linear functional of
the (invariant) joint distribution of two successive observations is
defined using the pairs of successive observations. Its efficiency is
proved using a martingale approximation. As a corollary we show effici
ency of the empirical joint distribution function in the sense of a fu
nctional convolution theorem.