  The setting is a stationary, ergodic time series. The challenge is to
construct a sequence of functions, each based on only finite segments of the
past, which together provide a strongly consistent estimator for the
conditional probability of the next observation, given the infinite past.
Ornstein gave such a construction for the case that the values are from a
finite set, and recently Algoet extended the scheme to time series with
coordinates in a Polish space.
  The present study relates a different solution to the challenge. The
algorithm is simple and its verification is fairly transparent. Some extensions
to regression, pattern recognition, and on-line forecasting are mentioned.
