Near-ideal causal smoothing filters for the real sequences

Abstract

The paper considers causal smoothing of the real sequences, i.e., discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal ideal smoothing filters with transfer functions vanishing at a point of the unit circle and such that they transfer processes into predictable ones. In this sense, the suggested filters are near-ideal; a faster gain decay would lead to the loss of causality. Applications to predicting algorithms are discussed and illustrated by experiments with forecasting of autoregressions with the coefficients that are deemed to be untraceable.