Estimating the residual waiting time for binary stationary time series

We present here a universal estimation scheme for the problem of estimating the residual waiting time until the next occurrence of a zero after observing the first n outputs of a stationary and ergodic binary process. The scheme will involve estimating only at carefully selected stopping times but will be almost surely consistent. In case the process happens to be a genuine renewal process then our stopping times will have asymptotic density one.