  We consider the problem of online estimation of a real-valued signal
corrupted by oblivious zero-mean noise using linear estimators. The estimator
is required to iteratively predict the underlying signal based on the current
and several last noisy observations, and its performance is measured by the
mean-square-error. We describe and analyze an algorithm for this task which: 1.
Achieves logarithmic adaptive regret against the best linear filter in
hindsight. This bound is assyptotically tight, and resolves the question of
Moon and Weissman [1]. 2. Runs in linear time in terms of the number of filter
coefficients. Previous constructions required at least quadratic time.
