Sub-ideal causal smoothing filters for real sequences

TL;DR

This paper introduces a family of causal smoothing filters for real sequences that approximate non-causal filters with desirable predictability properties, balancing gain decay and causality for improved forecasting.

Contribution

It proposes near-ideal causal filters with transfer functions vanishing at a point on the unit circle, enhancing predictability in deterministic sequences.

Findings

Filters effectively approximate non-causal smoothing with improved predictability.

Experimental results demonstrate successful forecasting of autoregressive processes.

The approach balances causality and gain decay for practical predictive applications.

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 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.