  The problem of predicting a sequence $x_1,x_2,...$ generated by a discrete
source with unknown statistics is considered. Each letter $x_{t+1}$ is
predicted using information on the word $x_1x_2... x_t$ only. In fact, this
problem is a classical problem which has received much attention. Its history
can be traced back to Laplace. We address the problem where each $x_i$ belongs
to some large (or even infinite) alphabet. A method is presented for which the
precision is greater than for known algorithms, where precision is estimated by
the Kullback-Leibler divergence. The results can readily be translated to
results about adaptive coding.
