  The problem of filtering of finite-alphabet stationary ergodic time series is
considered. A method for constructing a confidence set for the (unknown) signal
is proposed, such that the resulting set has the following properties: First,
it includes the unknown signal with probability $\gamma$, where $\gamma$ is a
parameter supplied to the filter. Second, the size of the confidence sets grows
exponentially with the rate that is asymptotically equal to the conditional
entropy of the signal given the data. Moreover, it is shown that this rate is
optimal.
