  The conditional distribution of the next outcome given the infinite past of a
stationary process can be inferred from finite but growing segments of the
past. Several schemes are known for constructing pointwise consistent
estimates, but they all demand prohibitive amounts of input data. In this paper
we consider real-valued time series and construct conditional distribution
estimates that make much more efficient use of the input data. The estimates
are consistent in a weak sense, and the question whether they are pointwise
consistent is still open. For finite-alphabet processes one may rely on a
universal data compression scheme like the Lempel-Ziv algorithm to construct
conditional probability mass function estimates that are consistent in expected
information divergence. Consistency in this strong sense cannot be attained in
a universal sense for all stationary processes with values in an infinite
alphabet, but weak consistency can. Some applications of the estimates to
on-line forecasting, regression and classification are discussed.
